| Title: | Periodically Correlated and Periodically Integrated Time Series |
|---|---|
| Description: | Classes and methods for modelling and simulation of periodically correlated (PC) and periodically integrated time series. Compute theoretical periodic autocovariances and related properties of PC autoregressive moving average models. Some original methods including Boshnakov & Iqelan (2009) <doi:10.1111/j.1467-9892.2009.00617.x>, Boshnakov (1996) <doi:10.1111/j.1467-9892.1996.tb00281.x>. |
| Authors: | Georgi N. Boshnakov [aut, cre] |
| Maintainer: | Georgi N. Boshnakov <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.15.2.9000 |
| Built: | 2025-01-25 04:20:07 UTC |
| Source: | https://github.com/geobosh/pcts |
Classes and methods for modelling and simulation of periodically correlated (PC) and periodically integrated time series. Compute theoretical periodic autocovariances and related properties of PC autoregressive moving average models. Some original methods including Boshnakov & Iqelan (2009) <doi:10.1111/j.1467-9892.2009.00617.x>, Boshnakov (1996) <doi:10.1111/j.1467-9892.1996.tb00281.x>.
The underlying assumption is that the observations are made at regular
intervals, such as quarter, month, week, day — or represent data for
such intervals — and these intervals are nested into larger periods.
In pcts we call the larger period a cycle and its parts seasons. Typical
examples of season-cycle timing are months in a year, quarters in a
year, days in a week (or business week). The number of seasons in a
cycle is called frequency in class "ts" in base R.
Cycles in pcts keep not only the number of seasons (frequency) but other
information, such as the names of the seasons and units of seasons. In
pcts there are a number of builtin cycle classes for typical cases, as
well as provision for creation of custom cycles on the fly. See
pcCycle and BuiltinCycle for ways to create
cycle objects, and allSeasons for further examples.
Periodic time series can be created with pcts, which
accepts as input vectors, matrices and time series objects from base R
and some other packages, including zoo and xts. When importing data,
the time information is taken from the data and an attempt is made to
guess the periodicity from the frequency (for time series objects that
have it set) and an analysis of the datetime stamps, if present.
pcts also has arguments for specifying the number of seasons or
the cycle, as well as the start datetime.
The main periodic time series classes in pcts are
PeriodicTS and PeriodicMTS,
for univariate and multivariate time series, respectively. Standard
base-R time series functions can be used with them directly, see for
example
window,
frequency,
cycle,
time,
deltat,
start,
end,
boxplot,
monthplot,
na.trim (na.trim is from package zoo).
Methods for
plot,
summary,
print,
show,
head,
tail,
and other base-R functions are defined where suitable. Examples can be
found in section Examples and in help pages for the corresponding
functions, classes and methods.
The naming conventions are as follows. Names of classes generally consists of one or more words. The first letter of each word, is capitalised. Only the first letter of abbreviations for models, such as ARMA, is capitalised. Similarly for generic functions but for them the first word is not capitalised. In a few names PM stands for 'periodic model' and TS for 'time series'.
Significant portion of the code was written in 2005–2007. Many of the functions and classes have been renamed under the above conventions and most of those that are not are not exported but a few still are and they should be considered subject to change.
autocovariances, autocorrelations, partialAutocorrelations
and others are one-stop generic functions for computation of properties
of time series and models. What to compute is deduced from the type of
the object. For models they compute theoretical quantities — periodic
or non-periodic, scalar or multivariate. For time series they compute
the corresponding sample counterparts.
Georgi N. Boshnakov [aut, cre]
Maintainer: Georgi N. Boshnakov <[email protected]>
Boshnakov GN (1994).
“Periodically Correlated Sequences: Some Properties and Recursions.”
Research Report 1, Division of Quality Technology and Statistics, Luleo University, Sweden.
Boshnakov GN (1996).
“The asymptotic covariance matrix of the multivariate serial correlations.”
Stochastic Process. Appl., 65(2), 251–258.
ISSN 0304-4149, doi:10.1016/S0304-4149(96)00104-4.
Boshnakov GN (1996).
“Recursive computation of the parameters of periodic autoregressive moving-average processes.”
J. Time Ser. Anal., 17(4), 333–349.
ISSN 0143-9782, doi:10.1111/j.1467-9892.1996.tb00281.x.
Boshnakov GN (1997).
“Periodically correlated solutions to a class of stochastic difference equations.”
In Csiszar I, Michaletzky G (eds.), Stochastic differential and difference equations (Gyor, 1996), volume 23 of Progr. Systems Control Theory, 1–9.
Birkhauser Boston, Boston, MA.
Boshnakov GN (2002).
“Multi-companion matrices.”
Linear Algebra Appl., 354, 53–83.
ISSN 0024-3795, doi:10.1016/S0024-3795(01)00475-X.
Boshnakov GN, Boteva A (1992).
“An algorithm for the computation of the theoretical autocovariances of a periodic autoregression process.”
Varna.
Boshnakov GN, Iqelan BM (2009).
“Generation of time series models with given spectral properties.”
J. Time Series Anal., 30(3), 349–368.
ISSN 0143-9782, doi:10.1111/j.1467-9892.2009.00617.x.
Boshnakov GN, Iqelan BM (2012).
“Maximum entropy models for general lag patterns.”
Journal of Time Series Analysis, 33(1), 112–120.
ISSN 1467-9892, doi:10.1111/j.1467-9892.2011.00744.x.
Boshnakov GN, Lambert-Lacroix S (2009).
“Maximum entropy for periodically correlated processes from nonconsecutive autocovariance coefficients.”
J. Time Series Anal., 30(5), 467–486.
doi:10.1111/j.1467-9892.2009.00619.x.
Boshnakov GN, Lambert-Lacroix S (2011).
pcme: Maximum entropy estimation of periodically correlated time series.
R package version 0.55, https://personalpages.manchester.ac.uk/staff/georgi.boshnakov/Rpackages/.
Boshnakov GN, Lambert-Lacroix S (2012).
“A periodic Levinson-Durbin algorithm for entropy maximization.”
Computational Statistics & Data Analysis, 56, 15–24.
ISSN 0167-9473, doi:10.1016/j.csda.2011.07.001, https://www.sciencedirect.com/science/article/pii/S0167947311002556.
Boswijk HP, Franses PH (1996).
“Unit roots in periodic autoregressions.”
Journal of Time Series Analysis, 17(3), 221–245.
Francq C, Roy R, Saidi A (2011).
“Asymptotic properties of weighted least squares estimation in weak parma models.”
Journal of Time Series Analysis, 32(6), 699–723.
Franses PH (1996).
Periodicity and Stochastic Trends In Economic Time Series.
Oxford University Press Inc., New York.
Franses PH, Paap R (2004).
Periodic Time Series Models.
Oxford University Press Inc., New York.
Grolemund G, Wickham H (2011).
“Dates and Times Made Easy with lubridate.”
Journal of Statistical Software, 40(3), 1–25.
doi:10.18637/jss.v040.i03.
Hipel KW, McLeod AI (1994).
Time series modelling of water resources and environmental systems, Developments in water science; 45.
London; Amsterdam: Elsevier.
Lambert-Lacroix S (2000).
“On periodic autoregressive process estimation.”
IEEE Transactions on Signal Processing, 48(6), 1800-1803.
Lambert-Lacroix S (2005).
“Extension of autocovariance coefficients sequence for periodically correlated processes.”
Journal of Time Series Analysis, 26(3), 423-435.
Lancaster P, Tismenetsky M (1985).
The theory of matrices, Second edition.
Academic Press, New York.
McLeod AI (1993).
“Parsimony, model adequacy and periodic correlation in time series forecasting.”
Internat. Statist. Rev., 61(3), 387-393.
McLeod AI (1993).
“Parsimony, model adequacy and periodic correlation in time series forecasting.”
Internat. Statist. Rev., 61(3), 387-393.
McLeod AI (1994).
“Diagnostic checking of periodic autoregression models with application.”
Journal of Time Series Analysis, 15(2), 221–233.
McLeod AI (1995).
“Diagnostic checking of periodic autoregression models with application.”
Journal of Time Series Analysis, 16(6), 647-648.
doi:10.1111/j.1467-9892.1995.tb00260.x, This corrects some typos in the eponimous article McLeod (1994).
Pagano M (1978).
“On periodic and multiple autoregression.”
Ann. Statist., 6, 1310-1317.
pcts,
dataFranses1996, Fraser2017,
four_stocks_since2016_01_01,
data(dataFranses1996) class(dataFranses1996) # [1] "mts" "ts" "matrix" pcfr <- pcts(dataFranses1996) class(pcfr) # "PeriodicMTS" nSeasons(pcfr) # 4 allSeasons(pcfr) allSeasons(pcfr, abb = TRUE) ## subsetting ## one index, x[i], is analogous to lists pcfr2to4 <- pcfr[2:4]; class(pcfr2to4) # "PeriodicMTS" pcfr2to2 <- pcfr[2]; class(pcfr2to2) # "PeriodicMTS" pcfr2 <- pcfr[[2]]; class(pcfr2) # note '[[', "PeriodicTS" ## data for 1990 quarter 3 pcfr2to4[as_date("1990-07-01")] # note: not "1990-03-01"! pct1990_Q3 <- Pctime(c(1990, 3), pcCycle(pcfr2to4)) pcfr2to4[pct1990_Q3] ## with empty index, returns the underlying data dim(pcfr[]) # [1] 148 19 dim(pcfr2to2[]) # 148 1 length(pcfr2[]) # 148 (this is numeric) summary(pcfr2) summary(pcfr2to4) ## make the output width shorter summary(pcfr2to4, row.names = FALSE) summary(pcfr2to4, row.names = 5) # trim row names to 5 characters head(pcfr2to4) # starts with NA's tail(pcfr2to4) # some NA's at the end too ## time of first and last data, may be NA's start(pcfr2to4) # 1955 Q1 end(pcfr2to4) # 1991 Q4 ## time of first nonNA: availStart(pcfr2) # 1955 Q1 availStart(pcfr2to4) # 1955 Q1 ## time of last nonNA: availEnd(pcfr[[2]]) # 1991 Q4 availEnd(pcfr[[3]]) # 1987 Q4 availEnd(pcfr[[4]]) # 1990 Q4 ## but at least one of them is available for 1991 Q4, so: availEnd(pcfr2to4) # 1991 Q4 ## use window() to pick part of the ts by time: window(pcfr2to4, start = c(1990, 1), end = c(1991, 4)) ## drop NA's at the start and end: window(pcfr2to4, start = availStart(pcfr2to4), end = availEnd(pcfr2to4)) plot(pcfr2) # the points mark the first season in each cycle boxplot(pcfr2) monthplot(pcfr2)data(dataFranses1996) class(dataFranses1996) # [1] "mts" "ts" "matrix" pcfr <- pcts(dataFranses1996) class(pcfr) # "PeriodicMTS" nSeasons(pcfr) # 4 allSeasons(pcfr) allSeasons(pcfr, abb = TRUE) ## subsetting ## one index, x[i], is analogous to lists pcfr2to4 <- pcfr[2:4]; class(pcfr2to4) # "PeriodicMTS" pcfr2to2 <- pcfr[2]; class(pcfr2to2) # "PeriodicMTS" pcfr2 <- pcfr[[2]]; class(pcfr2) # note '[[', "PeriodicTS" ## data for 1990 quarter 3 pcfr2to4[as_date("1990-07-01")] # note: not "1990-03-01"! pct1990_Q3 <- Pctime(c(1990, 3), pcCycle(pcfr2to4)) pcfr2to4[pct1990_Q3] ## with empty index, returns the underlying data dim(pcfr[]) # [1] 148 19 dim(pcfr2to2[]) # 148 1 length(pcfr2[]) # 148 (this is numeric) summary(pcfr2) summary(pcfr2to4) ## make the output width shorter summary(pcfr2to4, row.names = FALSE) summary(pcfr2to4, row.names = 5) # trim row names to 5 characters head(pcfr2to4) # starts with NA's tail(pcfr2to4) # some NA's at the end too ## time of first and last data, may be NA's start(pcfr2to4) # 1955 Q1 end(pcfr2to4) # 1991 Q4 ## time of first nonNA: availStart(pcfr2) # 1955 Q1 availStart(pcfr2to4) # 1955 Q1 ## time of last nonNA: availEnd(pcfr[[2]]) # 1991 Q4 availEnd(pcfr[[3]]) # 1987 Q4 availEnd(pcfr[[4]]) # 1990 Q4 ## but at least one of them is available for 1991 Q4, so: availEnd(pcfr2to4) # 1991 Q4 ## use window() to pick part of the ts by time: window(pcfr2to4, start = c(1990, 1), end = c(1991, 4)) ## drop NA's at the start and end: window(pcfr2to4, start = availStart(pcfr2to4), end = availEnd(pcfr2to4)) plot(pcfr2) # the points mark the first season in each cycle boxplot(pcfr2) monthplot(pcfr2)
Indexing of objects from classes in package pcts.
signature(x = "BasicCycle", i = "ANY", j = "missing", drop = "ANY")signature(x = "BasicCycle", i = "missing", j = "missing", drop = "ANY")signature(x = "PeriodicMTS", i = "ANY", j = "missing", drop = "ANY")signature(x = "PeriodicMTS", i = "missing", j = "missing", drop = "ANY")signature(x = "PeriodicVector", i = "ANY", j = "ANY", drop = "ANY")signature(x = "PeriodicVector", i = "ANY", j = "missing", drop = "ANY")signature(x = "PeriodicVector", i = "missing", j = "ANY", drop = "ANY")signature(x = "PeriodicVector", i = "missing", j = "missing",
drop = "ANY")signature(x = "VirtualPeriodicAutocovarianceModel", i = "missing",
j = "missing", drop = "ANY")signature(x = "VirtualPeriodicAutocovarianceModel", i = "missing",
j = "numeric", drop = "ANY")signature(x = "VirtualPeriodicAutocovarianceModel", i = "numeric",
j = "missing", drop = "ANY")signature(x = "VirtualPeriodicAutocovarianceModel", i = "numeric",
j = "numeric", drop = "ANY")signature(x = "PeriodicTS", i = "missing", j = "missing", drop = "ANY")signature(x = "PeriodicMTS", i = "ANY", j = "ANY", drop = "ANY")signature(x = "PeriodicMTS", i = "AnyDateTime", j = "ANY", drop = "ANY")signature(x = "PeriodicMTS", i = "AnyDateTime", j = "missing",
drop = "ANY")signature(x = "PeriodicTS", i = "AnyDateTime", j = "missing",
drop = "ANY")Georgi N. Boshnakov
`[[` in package 'pcts'Methods for function`[[` in package 'pcts'.
signature(x = "PeriodicMTS", i = "ANY", j = "ANY")signature(x = "VirtualPeriodicAutocovarianceModel", i = "numeric",
j = "ANY")Index assignments for objects from classes in package pcts.
signature(x = "PeriodicVector", i = "ANY", j = "ANY", value = "ANY")signature(x = "PeriodicVector", i = "missing", j = "ANY", value = "ANY")signature(x = "BasicCycle", i = "ANY", j = "missing", value = "ANY")signature(x = "BasicCycle", i = "missing", j = "missing", value = "ANY")signature(x = "PeriodicAutocovarianceModel", i = "ANY", j = "ANY",
value = "ANY")Georgi N. Boshnakov
$ in package 'pcts'Methods for function$ in package 'pcts'.
signature(x = "PeriodicMTS")Functions and methods fo get names of seasons and related quantities for objects from the cycle, periodic time series classes and other objects for which the concepts are defined.
unitSeason(x) unitCycle(x) seqSeasons(x) allSeasons(x, abb = FALSE, prefix = "S", ...) unitSeason ( x, ... ) <- value unitCycle ( x, ... ) <- value allSeasons ( x, abb, ... ) <- value ## S4 replacement method for signature 'SimpleCycle' allSeasons(x, abb, prefix, ...) <- value ## S4 replacement method for signature 'Cyclic' allSeasons(x, abb = FALSE, ...) <- valueunitSeason(x) unitCycle(x) seqSeasons(x) allSeasons(x, abb = FALSE, prefix = "S", ...) unitSeason ( x, ... ) <- value unitCycle ( x, ... ) <- value allSeasons ( x, abb, ... ) <- value ## S4 replacement method for signature 'SimpleCycle' allSeasons(x, abb, prefix, ...) <- value ## S4 replacement method for signature 'Cyclic' allSeasons(x, abb = FALSE, ...) <- value
x |
a cycle, time series or other object for which the concept of seasons is defined. |
abb |
if |
prefix |
use this prefix for automatically generated names of seasons. |
... |
further arguments for methods. |
value |
a character string |
The cycle classes, i.e. classes inheriting from class
BasicCycle, provide common functionality. In
particular, they guarantee that the functions described in this topic
are available. These functions work also for the periodic time series
classes and may be defined for other classes where they make sense.
Methods for allSeasons():
signature(x = "BasicCycle", abb = "ANY")signature(x = "DayWeekCycle", abb = "logical")signature(x = "DayWeekCycle", abb = "missing")signature(x = "MonthYearCycle", abb = "logical")signature(x = "MonthYearCycle", abb = "missing")signature(x = "OpenCloseCycle", abb = "logical")signature(x = "OpenCloseCycle", abb = "missing")signature(x = "QuarterYearCycle", abb = "logical")signature(x = "QuarterYearCycle", abb = "missing")signature(x = "SimpleCycle", abb = "ANY")signature(x = "Cyclic", abb = "ANY")signature(x = "Every30MinutesCycle", abb = "logical")signature(x = "Every30MinutesCycle", abb = "missing")signature(x = "VirtualPeriodicModel", abb = "ANY")Georgi N. Boshnakov
opcycle <- new("OpenCloseCycle") ## convert to SimpleCycle to change some names siopcycle <- as(opcycle, "SimpleCycle") ## siopcycle inherits names from opcycle unitSeason(siopcycle) # "Season" unitCycle(siopcycle) # "Cycle" allSeasons(siopcycle) # "Open" "Close" allSeasons(siopcycle, abb = TRUE) # "O" "C" allSeasons(siopcycle) <- c("Day", "Night") allSeasons(siopcycle) # now: "Day" "Night" ## change also abbreviations allSeasons(siopcycle, abb = TRUE) <- c("D", "N") allSeasons(siopcycle, abb = TRUE) # now: "D" "N" seasons <- new("SimpleCycle", 4) unitSeason(seasons) # "Season" unitCycle(seasons) # "Cycle" allSeasons(seasons) allSeasons(seasons, abb = TRUE) unitCycle(seasons) <- "Year" unitCycle(seasons) allSeasons(seasons) <- c("Winter", "Spring", "Summer", "Autumn") allSeasons(seasons) allSeasons(seasons, abb = TRUE) <- c("Win", "Spr", "Sum", "Aut") allSeasons(seasons, abb = TRUE) ## change autumn to Fall allSeasons(seasons)[4] <- "Fall" allSeasons(seasons, abb = TRUE)[4] <- "Fal" allSeasons(seasons) allSeasons(seasons, abb = TRUE) ## indexing of cycle objects is equivalent to allSeasons. seasons[] seasons[ , abb = TRUE] seasons[4] <- "Herbst" seasons unitCycle(seasons) <- "Jahre" unitCycle(seasons) unitSeason(seasons) <- "Jahreszeit" seasons[] <- c("Winter", "Frueling", "Sommer", "Herbst") seasons[ , abb = TRUE] <- c("W", "F", "S", "H") seasons[] seasonsopcycle <- new("OpenCloseCycle") ## convert to SimpleCycle to change some names siopcycle <- as(opcycle, "SimpleCycle") ## siopcycle inherits names from opcycle unitSeason(siopcycle) # "Season" unitCycle(siopcycle) # "Cycle" allSeasons(siopcycle) # "Open" "Close" allSeasons(siopcycle, abb = TRUE) # "O" "C" allSeasons(siopcycle) <- c("Day", "Night") allSeasons(siopcycle) # now: "Day" "Night" ## change also abbreviations allSeasons(siopcycle, abb = TRUE) <- c("D", "N") allSeasons(siopcycle, abb = TRUE) # now: "D" "N" seasons <- new("SimpleCycle", 4) unitSeason(seasons) # "Season" unitCycle(seasons) # "Cycle" allSeasons(seasons) allSeasons(seasons, abb = TRUE) unitCycle(seasons) <- "Year" unitCycle(seasons) allSeasons(seasons) <- c("Winter", "Spring", "Summer", "Autumn") allSeasons(seasons) allSeasons(seasons, abb = TRUE) <- c("Win", "Spr", "Sum", "Aut") allSeasons(seasons, abb = TRUE) ## change autumn to Fall allSeasons(seasons)[4] <- "Fall" allSeasons(seasons, abb = TRUE)[4] <- "Fal" allSeasons(seasons) allSeasons(seasons, abb = TRUE) ## indexing of cycle objects is equivalent to allSeasons. seasons[] seasons[ , abb = TRUE] seasons[4] <- "Herbst" seasons unitCycle(seasons) <- "Jahre" unitCycle(seasons) unitSeason(seasons) <- "Jahreszeit" seasons[] <- c("Winter", "Frueling", "Sommer", "Herbst") seasons[ , abb = TRUE] <- c("W", "F", "S", "H") seasons[] seasons
Replace methods for as_date in package pcts.
signature(x = "PeriodicTimeSeries")signature(x = "ANY")signature(x = "character")signature(x = "Cyclic")signature(x = "numeric")signature(x = "POSIXt")Methods for as_datetime in package pcts.
signature(x = "PeriodicTimeSeries")Methods for computation of autocorrelations and periodic autocorrelations.
signature(x = "numeric", maxlag = "ANY", lag_0 = "missing")signature(x = "PeriodicTimeSeries", maxlag = "ANY", lag_0 = "missing")signature(x = "PeriodicAutocovariances", maxlag = "ANY",
lag_0 = "missing")signature(x = "SamplePeriodicAutocovariances", maxlag = "ANY",
lag_0 = "missing")signature(x = "VirtualPeriodicAutocovariances", maxlag = "ANY",
lag_0 = "missing")signature(x = "VirtualPeriodicAutocovarianceModel", maxlag = "ANY",
lag_0 = "missing")autocorrelations in package sarima
for further details.
autocovariances for autocovariances;
## periodic ts object => peridic acf autocorrelations(pcts(AirPassengers), maxlag = 10) ## for "ts" or "numeric" objects the default is non-periodic acf autocorrelations(AirPassengers, maxlag = 10) autocorrelations(as.numeric(AirPassengers)) ## argument 'nseasons' forces periodic acf autocorrelations(AirPassengers, maxlag = 10, nseasons = 12) autocorrelations(as.numeric(AirPassengers), maxlag = 10, nseasons = 12)## periodic ts object => peridic acf autocorrelations(pcts(AirPassengers), maxlag = 10) ## for "ts" or "numeric" objects the default is non-periodic acf autocorrelations(AirPassengers, maxlag = 10) autocorrelations(as.numeric(AirPassengers)) ## argument 'nseasons' forces periodic acf autocorrelations(AirPassengers, maxlag = 10, nseasons = 12) autocorrelations(as.numeric(AirPassengers), maxlag = 10, nseasons = 12)
Methods for the generic function autocovariances(), which
computes autocovariances meaningful for the first argument. For
objects representing time series, it computes sample autocovariances
(univariate, multivariate, periodic, as appropriate). For objects
representing models, it computes the relevant theoretical
autocovariances.
signature(x = "matrix", maxlag = "ANY")signature(x = "numeric", maxlag = "ANY")signature(x = "PeriodicArmaModel", maxlag = "ANY")signature(x = "PeriodicArModel", maxlag = "ANY")signature(x = "PeriodicAutocovarianceModel", maxlag = "ANY")signature(x = "PeriodicTS", maxlag = "ANY")signature(x = "VirtualPeriodicAutocovariances", maxlag = "ANY")If maxlag is missing or equal to maxLag(x), x
is returned unchanged. Otherwise the number of available lags is
adjusted to maxlag.
autocovariances in package sarima
for further details.
autocorrelations for autocorrelations;
## periodic ts object => peridic acvf autocovariances(pcts(AirPassengers), maxlag = 10) ## for "ts" or "numeric" objects the default is non-periodic acvf autocovariances(AirPassengers, maxlag = 10) autocovariances(as.numeric(AirPassengers)) ## argument 'nseasons' forces periodic acvf autocovariances(AirPassengers, maxlag = 10, nseasons = 12) autocovariances(as.numeric(AirPassengers), maxlag = 10, nseasons = 12)## periodic ts object => peridic acvf autocovariances(pcts(AirPassengers), maxlag = 10) ## for "ts" or "numeric" objects the default is non-periodic acvf autocovariances(AirPassengers, maxlag = 10) autocovariances(as.numeric(AirPassengers)) ## argument 'nseasons' forces periodic acvf autocovariances(AirPassengers, maxlag = 10, nseasons = 12) autocovariances(as.numeric(AirPassengers), maxlag = 10, nseasons = 12)
Time of first or last non-NA value.
availStart(x, any = TRUE) availEnd(x, any = TRUE)availStart(x, any = TRUE) availEnd(x, any = TRUE)
x |
a time series or similar object |
any |
logical flag for multivariate objects. The default |
The time is given as a cycle-season pair.
Argument any is meaningful only for multivariate objects. Its
name is short for
"the first/last index for which any of the values (ie at least one) is non-NA".
any = FALSE is taken to mean that the index is the first/last
for which all values are non-NA.
The functions can be used together with windows to trim
NA's from the beginning and/or end of the data. As an
alternative we provide also methods for periodic time series methods
for zoo:na.trim, see the examples below.
numeric, length 2
tipi <- pcts(dataFranses1996[ , "USTotalIPI"]) start(tipi) end(tipi) head(tipi) tail(tipi) tipi <- window(tipi, start = availStart(tipi), end = availEnd(tipi)) start(tipi) end(tipi) plot(tipi) pcfr <- pcts(dataFranses1996) pcfr2to4 <- pcfr[2:4] head(pcfr2to4) tail(pcfr2to4) ## time of first and last data, can be NA's start(pcfr2to4) # 1955 Q1 end(pcfr2to4) # 1991 Q4 ## time of first nonNA: availStart(pcfr[[2]]) # 1960 Q1 availStart(pcfr2to4) # 1960 Q1 ## time of last nonNA: availEnd(pcfr[[2]]) # 1991 Q4 availEnd(pcfr[[3]]) # 1987 Q4 availEnd(pcfr[[4]]) # 1990 Q4 ## but at least one of them is available for 1991 Q4, so: availEnd(pcfr2to4) # 1991 Q4 ## this requests the time of the last full record: availEnd(pcfr2to4, any = FALSE) # 1987 Q4 pcfr2to4a <- window(pcfr2to4, start = availStart(pcfr2to4), end = availEnd(pcfr2to4)) head(pcfr2to4a) tail(pcfr2to4a, 20) ## trim NA's from both ends, up to the firsxst/last full record: pcfr2to4b <- window(pcfr2to4, start = availStart(pcfr2to4, FALSE), end = availEnd(pcfr2to4, FALSE)) ## TODO: need a better example here since the first non-NA value for all ## ts in pcfr2to4 is at the same ## alternatively, use na.trim(), the default for is.na is "any" pcpres <- window(pcts(presidents), end = c(1972, 4)) availStart(pcpres) # 1945 2 availEnd(pcpres) # 1972 2 both <- na.trim(pcpres) # same as "both" identical(na.trim(pcpres), both) # TRUE head(both, 7) tail(both) head(na.trim(pcpres, "left"), 7) tail(na.trim(pcpres, "right")) cguk <- pcfr[c("CanadaUnemployment", "GermanyGNP", "UKTotalInvestment")] availStart(cguk) availStart(cguk, TRUE) # same availStart(cguk, FALSE) availEnd(cguk) availEnd(cguk, TRUE) # same availEnd(cguk, FALSE) na.trim(cguk) head( na.trim(cguk, sides = "left") ) tail( na.trim(cguk, sides = "right") ) head( na.trim(cguk, sides = "left", is.na = "all") ) tail( na.trim(cguk, sides = "right", is.na = "all") )tipi <- pcts(dataFranses1996[ , "USTotalIPI"]) start(tipi) end(tipi) head(tipi) tail(tipi) tipi <- window(tipi, start = availStart(tipi), end = availEnd(tipi)) start(tipi) end(tipi) plot(tipi) pcfr <- pcts(dataFranses1996) pcfr2to4 <- pcfr[2:4] head(pcfr2to4) tail(pcfr2to4) ## time of first and last data, can be NA's start(pcfr2to4) # 1955 Q1 end(pcfr2to4) # 1991 Q4 ## time of first nonNA: availStart(pcfr[[2]]) # 1960 Q1 availStart(pcfr2to4) # 1960 Q1 ## time of last nonNA: availEnd(pcfr[[2]]) # 1991 Q4 availEnd(pcfr[[3]]) # 1987 Q4 availEnd(pcfr[[4]]) # 1990 Q4 ## but at least one of them is available for 1991 Q4, so: availEnd(pcfr2to4) # 1991 Q4 ## this requests the time of the last full record: availEnd(pcfr2to4, any = FALSE) # 1987 Q4 pcfr2to4a <- window(pcfr2to4, start = availStart(pcfr2to4), end = availEnd(pcfr2to4)) head(pcfr2to4a) tail(pcfr2to4a, 20) ## trim NA's from both ends, up to the firsxst/last full record: pcfr2to4b <- window(pcfr2to4, start = availStart(pcfr2to4, FALSE), end = availEnd(pcfr2to4, FALSE)) ## TODO: need a better example here since the first non-NA value for all ## ts in pcfr2to4 is at the same ## alternatively, use na.trim(), the default for is.na is "any" pcpres <- window(pcts(presidents), end = c(1972, 4)) availStart(pcpres) # 1945 2 availEnd(pcpres) # 1972 2 both <- na.trim(pcpres) # same as "both" identical(na.trim(pcpres), both) # TRUE head(both, 7) tail(both) head(na.trim(pcpres, "left"), 7) tail(na.trim(pcpres, "right")) cguk <- pcfr[c("CanadaUnemployment", "GermanyGNP", "UKTotalInvestment")] availStart(cguk) availStart(cguk, TRUE) # same availStart(cguk, FALSE) availEnd(cguk) availEnd(cguk, TRUE) # same availEnd(cguk, FALSE) na.trim(cguk) head( na.trim(cguk, sides = "left") ) tail( na.trim(cguk, sides = "right") ) head( na.trim(cguk, sides = "left", is.na = "all") ) tail( na.trim(cguk, sides = "right", is.na = "all") )
Methods for computation of periodic backward partial coefficients.
signature(x = "VirtualPeriodicAutocovariances")Compute periodic backward partial variances.
signature(x = "VirtualPeriodicAutocovariances")Class BareCycle.
Objects can be created by calls of the form pcCycle(nseasons)
or new("BareCycle", nseasons).
Class "BareCycle" represents the number of seasons and is
sufficient for many computations.
nseasons:Object of class "integer", the number
of seasons.
Class "BasicCycle", directly.
signature(.Object = "BareCycle"): ...
signature(from = "BareCycle", to = "SimpleCycle"): ...
signature(from = "BuiltinCycle", to = "BareCycle"): ...
signature(object = "BareCycle"): ...
signature(object = "BareCycle"): ...
Georgi N. Boshnakov
pcCycle for creation of cycle objects and extraction of
cycle part of time series,
BuiltinCycle-class,
SimpleCycle-class,
DayWeekCycle-class,
MonthYearCycle-class,
OpenCloseCycle-class,
QuarterYearCycle-class
PartialCycle-class,
BasicCycle-class (virtual, for use in signatures)
pcCycle(5) cycle <- new("BareCycle", 5) identical(new("BareCycle", 5), pcCycle(5)) # TRUE unitSeason(cycle) unitCycle(cycle) allSeasons(cycle) seqSeasons(cycle) cycle[] cycle[3] ## if cycle represents 5-days week one may prefer: BuiltinCycle(5)pcCycle(5) cycle <- new("BareCycle", 5) identical(new("BareCycle", 5), pcCycle(5)) # TRUE unitSeason(cycle) unitCycle(cycle) allSeasons(cycle) seqSeasons(cycle) cycle[] cycle[3] ## if cycle represents 5-days week one may prefer: BuiltinCycle(5)
Virtual class "BasicCycle" is a class union that can be used in
signatures of methods and classes when any of the cycle classes is
admissible as argument or slot.
A virtual Class: No objects may be created from it.
signature(x = "BasicCycle", i = "ANY", j = "missing", drop = "ANY")
signature(x = "BasicCycle", i = "missing", j = "missing", drop = "ANY")
signature(x = "BasicCycle", i = "ANY", j = "missing", value = "ANY")
signature(x = "BasicCycle", i = "missing", j = "missing", value = "ANY")
signature(x = "BasicCycle"): ...
signature(x = "BasicCycle", abb = "ANY")
signature(x = "BasicCycle")
signature(x = "BasicCycle", type = "character"): ...
signature(x = "BasicCycle", type = "missing"): ...
signature(x = "matrix", nseasons = "BasicCycle"): ...
signature(x = "numeric", nseasons = "BasicCycle"): ...
Georgi N. Boshnakov
BareCycle-class (just number of seasons),
SimpleCycle-class (named seasons),
BuiltinCycle-class (common cycles, e.g.,
DayWeekCycle-class,
MonthYearCycle-class,
OpenCloseCycle-class,
QuarterYearCycle-class),
PartialCycle-class (cycles obtained from others by
subsetting or otherwise)
showClass("BasicCycle")showClass("BasicCycle")
"BuiltinCycle" and its subclasses in package 'pcts'Class "BuiltinCycle" and its subclasses in package 'pcts'.
Class "BuiltinCycle" is a virtual Class: no objects may be
created from it. Class "BuiltinCycle" has several built-in
cycle subclasses. Objects from the subclasses can be created by calls
of the form new("className", first, ...), where
"className" is the name of the subclass. The optional argument
first can be used to designate a season to be considered first
in the cycle, by default the first.
The function BuiltinCycle provides a more convenient way
to generate objects from subclasses of class
"BuiltinCycle". Its argument is the number of seasons.
These classes are effectively unmodifiable, but the user can convert them to other cycle classes, e.g. class "SimpleCycle", and adapt as needed.
The subclasses of "BuiltinCycle" have definitions for all
methods promised by its superclass "BasicCycle".
Currently, the following builtin classes are defined:
| Name | Description | nSeasons |
"DayWeekCycle" |
weekdays | 7 |
"QuarterYearCycle" |
quarters in a year | 4 |
"MonthYearCycle" |
months in a year | 12 |
"Every30MinutesCycle" |
half-hour intervals in a day | 48 |
"OpenCloseCycle" |
start/end of a working day | 2 |
There is also a class "FiveDayWeekCycle" but it is deprecated
and will be removed in the near future. Use BuiltinCycle(5)
to create objects with equivalent functionality.
The class "BuiltinCycle" and its subclasses have a single
common slot:
first:Object of class "integer",
the index of the season to be treated as the first in a cycle.
Class "BuiltinCycle" extends class
"BasicCycle", directly.
Classes "DayWeekCycle", "Every30MinutesCycle",
"FiveDayWeekCycle", "OpenCloseCycle" and
"QuarterYearCycle"
extend:
Class "BuiltinCycle", directly.
Class "BasicCycle", by class "BuiltinCycle", distance 2.
Functions with methods for this class:
signature(from = "BuiltinCycle", to = "BareCycle"): ...
signature(from = "BuiltinCycle", to = "SimpleCycle"): ...
signature(.Object = "BuiltinCycle"): ...
signature(object = "BuiltinCycle"): ...
The functions to extract properties from objects from the builtin
cycle classes have identical signatures (except for the name of the
class). For example, for "QuarterYearCycle" the methods are as
follows:
signature(x = "QuarterYearCycle", abb = "logical"): ...
signature(x = "QuarterYearCycle", abb = "missing"): ...
signature(object = "QuarterYearCycle"): ...
signature(x = "QuarterYearCycle"): ...
signature(x = "QuarterYearCycle"): ...
The methods for the remaining builtin classes are the same with
"QuarterYearCycle" replaced suitably.
Georgi N. Boshnakov
BuiltinCycle,
pcCycle for creation of cycle objects and extraction of
cycle part of time series,
class PartialCycle for creating variants of the
builtin classes, e.g., 5-day weeks.
BareCycle-class,
SimpleCycle-class,
## class "DayWeekCycle" dwcycle <- BuiltinCycle(7) # new("DayWeekCycle") unitSeason(dwcycle) unitCycle(dwcycle) allSeasons(dwcycle) dwcycle[] # same allSeasons(dwcycle, abb = TRUE) dwcycle[ , abb = TRUE] # same dwcycle[2] dwcycle[2, abb = TRUE] seqSeasons(dwcycle) ## start the week on Sunday dws <- BuiltinCycle(7, first = 7) # new("DayWeekCycle", first = 7) dws[1] # "Sunday" allSeasons(dws) ## class "Every30MinutesCycle" cyc48 <- BuiltinCycle(48) # new("Every30MinutesCycle") nSeasons(cyc48) allSeasons(cyc48) ## class "FiveDayWeekCycle" is deprecated, use the equivalent: fdcycle <- BuiltinCycle(5) unitSeason(fdcycle) unitCycle(fdcycle) allSeasons(fdcycle) fdcycle[] # same allSeasons(fdcycle, abb = TRUE) fdcycle[ , abb = TRUE] # same fdcycle[2] fdcycle[2, abb = TRUE] seqSeasons(fdcycle) ## class "MonthYearCycle" mycycle <- BuiltinCycle(12) # new("MonthYearCycle") unitSeason(mycycle) unitCycle(mycycle) allSeasons(mycycle) mycycle[ ] # same allSeasons(mycycle, , abb = TRUE) mycycle[ , abb = TRUE] # same mycycle[2] mycycle[2, abb = TRUE] seqSeasons(mycycle) ## class "OpenCloseCycle" opcycle <- new("OpenCloseCycle") unitSeason(opcycle) unitCycle(opcycle) allSeasons(opcycle) opcycle[ , abb = FALSE] # same allSeasons(opcycle, abb = FALSE) opcycle[] # same opcycle[2] opcycle[2, abb = TRUE] seqSeasons(opcycle) ## class "QuarterYearCycle" qycycle <- new("QuarterYearCycle") unitSeason(qycycle) unitCycle(qycycle) allSeasons(qycycle) qycycle[] # same allSeasons(qycycle, abb = TRUE) qycycle[ , abb = TRUE] # same qycycle[2] qycycle[2, abb = TRUE] seqSeasons(qycycle)## class "DayWeekCycle" dwcycle <- BuiltinCycle(7) # new("DayWeekCycle") unitSeason(dwcycle) unitCycle(dwcycle) allSeasons(dwcycle) dwcycle[] # same allSeasons(dwcycle, abb = TRUE) dwcycle[ , abb = TRUE] # same dwcycle[2] dwcycle[2, abb = TRUE] seqSeasons(dwcycle) ## start the week on Sunday dws <- BuiltinCycle(7, first = 7) # new("DayWeekCycle", first = 7) dws[1] # "Sunday" allSeasons(dws) ## class "Every30MinutesCycle" cyc48 <- BuiltinCycle(48) # new("Every30MinutesCycle") nSeasons(cyc48) allSeasons(cyc48) ## class "FiveDayWeekCycle" is deprecated, use the equivalent: fdcycle <- BuiltinCycle(5) unitSeason(fdcycle) unitCycle(fdcycle) allSeasons(fdcycle) fdcycle[] # same allSeasons(fdcycle, abb = TRUE) fdcycle[ , abb = TRUE] # same fdcycle[2] fdcycle[2, abb = TRUE] seqSeasons(fdcycle) ## class "MonthYearCycle" mycycle <- BuiltinCycle(12) # new("MonthYearCycle") unitSeason(mycycle) unitCycle(mycycle) allSeasons(mycycle) mycycle[ ] # same allSeasons(mycycle, , abb = TRUE) mycycle[ , abb = TRUE] # same mycycle[2] mycycle[2, abb = TRUE] seqSeasons(mycycle) ## class "OpenCloseCycle" opcycle <- new("OpenCloseCycle") unitSeason(opcycle) unitCycle(opcycle) allSeasons(opcycle) opcycle[ , abb = FALSE] # same allSeasons(opcycle, abb = FALSE) opcycle[] # same opcycle[2] opcycle[2, abb = TRUE] seqSeasons(opcycle) ## class "QuarterYearCycle" qycycle <- new("QuarterYearCycle") unitSeason(qycycle) unitCycle(qycycle) allSeasons(qycycle) qycycle[] # same allSeasons(qycycle, abb = TRUE) qycycle[ , abb = TRUE] # same qycycle[2] qycycle[2, abb = TRUE] seqSeasons(qycycle)
Create objects from class Cyclic.
Cyclic(cycle, start = NULL, ...) ## S3 method for class 'Cyclic' as.Date(x, ...) ## S3 method for class 'Cyclic' date(x) ## S3 method for class 'PeriodicTimeSeries' as.Date(x, ...)Cyclic(cycle, start = NULL, ...) ## S3 method for class 'Cyclic' as.Date(x, ...) ## S3 method for class 'Cyclic' date(x) ## S3 method for class 'PeriodicTimeSeries' as.Date(x, ...)
cycle |
a cycle object, a positive integer giving the number of seasons, or
any other object that can be used to create a cycle with
|
start |
a cycle-season pair, a datetime object, a Date object or any object
that can be converted to datetime with |
... |
for |
x |
a Cyclic object |
for Cyclic, an object from class "Cyclic"
BuiltinCycle, pcCycle for creation of cycle objects,
pcts importing and creating periodic time series
## bare bone Cyclic starting at Cycle 1, season 1 Cyclic(4) Cyclic(4, c(1,1)) # same ## with quarter/year cycle qu <- Cyclic(BuiltinCycle(4), start = c(2020, 1)) start(qu) as_datetime(qu) date(qu) <- c(2009, 2) qu ap <- pcts(AirPassengers) as.Date(ap)## bare bone Cyclic starting at Cycle 1, season 1 Cyclic(4) Cyclic(4, c(1,1)) # same ## with quarter/year cycle qu <- Cyclic(BuiltinCycle(4), start = c(2020, 1)) start(qu) as_datetime(qu) date(qu) <- c(2009, 2) qu ap <- pcts(AirPassengers) as.Date(ap)
"Cyclic"
Class "Cyclic"
Objects can be created by calls of the form new("Cyclic", ...).
cycle:Object of class "BasicCycle" ~~
pcstart:Object of class "ANY" ~~
signature(x = "Cyclic", abb = "ANY"): ...
signature(x = "Cyclic"): ...
signature(x = "Cyclic"): ...
signature(from = "PeriodicMTS", to = "Cyclic"): ...
signature(from = "PeriodicTS", to = "Cyclic"): ...
signature(from = "PeriodicMTS", to = "Cyclic"): ...
signature(from = "PeriodicTS", to = "Cyclic"): ...
signature(x = "Cyclic"): ...
signature(object = "Cyclic"): ...
signature(x = "Cyclic"): ...
signature(x = "Cyclic", type = "ANY"): ...
signature(x = "Cyclic"): ...
signature(object = "Cyclic"): ...
signature(x = "Cyclic"): ...
signature(x = "Cyclic"): ...
signature(x = "Cyclic"): ...
signature(x = "Cyclic"): ...
Pctime for conversion from/to dates and datetimes.
showClass("Cyclic")showClass("Cyclic")
A multivariate time series containing the data used in examples by Franses (1996).
data("dataFranses1996")data("dataFranses1996")
A multivariate quarterly time series.
Each column is a quarterly time series. The time series start and end
at different times, so NA's are used to align them in a single
multivariate time series. Detailed account of the sources of the data
is given by
@FransesB1; Data Appendix), p. 214.
year(column 1)
The time formatted as yyyy.Q, where yyyy is the year
and Q is the quarter (one of 1, 2, 3 or 4.). This column
was part of the original data but is not really needed here since
the time series object contains the time information.
USTotalIPI(column 2)
Total Industrial Production Index for the United States (1985 = 100), 1960.1–1991.4.
CanadaUnemployment(column 3)
Unemployment in Canada, measured in 1000 persons, 1960.1 - 1987.4.
GermanyGNP(column 4)
Real GNP in Germany, 1960.1 - 1990.4 .
UKTotalInvestment(column 5)
Real Total Investment in the United Kindom, 1955.1 - 1988.4.
SA_USTotalIPI (column 6)
Seasonally adjusted USTotalIPI.
SA_CanadaUnemployment(column 7)
Seasonally adjusted CanadaUnemployment.
SA_GermanyGNP(column 8)
Seasonally adjusted GermanyGNP.
UKGDP(column 9)
United Kingdom gross domestic product (at 1985 prices), 1955.1–1988.4.
UKTotalConsumption(column 10)
United Kingdom total consumption (at 1985 prices), 1955.1–1988.4.
UKNondurablesConsumption(column 11)
United Kindom nondurables consumption (at 1985 prices), 1955.1–1988.4.
UKExport(column 12)
United Kindom exports of goods and services (at 1985 prices), 1955.1–1988.4.
UKImport(column 13)
United Kindom imports of goods and services (at 1985 prices), 1955.1–1988.4.
UKPublicInvestment(column 14)
United Kindom public investment (at 1985 prices), 1962.1–1988.4.
UKWorkforce(column 15)
United Kindom workforce (consisting of workforce in employment and unemployment), 1955.1–1988.4.
SwedenNondurablesConsumption(column 16)
Real per capita non-durables consumption in Sweden (measured in logs), 1963.1–1988.1.
SwedenDisposableIncome(column 17)
Real per capita disposable income in Sweden (measured in logs), 1963.1–1988.1.
SA_SwedenNondurablesConsumption(column 18)
Seasonally adjusted SwedenNondurablesConsumption with
Census X-11 method, 1964.1–1988.1. (Using the approximate linear
Census X-11 filter given in Table 4.1, p. 52 in
Franses (1996) and generating the forecasts
and backcasts as described in Ooms (1994)).
SA_SwedenDisposableIncome(column 19)
Seasonally adjusted SwedenDisposableIncome with Census X-11
method, 1964.1–1988.1. (Using the same method as above.)
More details on the individual time series are given by Franses (1996).
Most of the time series in dataFranses1996 are available as
separate datasets in package ‘partsm’. The numbers should be the same
but note that, at the time of writing this, not all datasets there
carry complete time information.
The data were downloaded from
http://people.few.eur.nl/franses/research/data/data1.txt,
but this link is now broken.
Franses PH (1996). Periodicity and Stochastic Trends In Economic Time Series. Oxford University Press Inc., New York.
Fraser2017,
four_stocks_since2016_01_01
data(dataFranses1996) class(dataFranses1996) colnames(dataFranses1996) dim(dataFranses1996) # c(148, 19) plot(dataFranses1996[ , 2:11]) tipi <- dataFranses1996[ , "USTotalIPI"] plot(tipi) ## convert to PeriodicTS and remove NA's at the start and end pctipi <- pcts(tipi) pctipi <- window(pctipi, start = availStart(pctipi), end = availEnd(pctipi)) plot(pctipi) ## convert the whole dataset to class "PeriodicMTS" pcfr <- pcts(dataFranses1996) colnames(pcfr)[2:3] # "USTotalIPI" "CanadaUnemployment" ## subset as "PeriodicMTS" pcfr2to3 <- pcfr[2:3] plot(pcfr2to3) ## "[" "PeriodicMTS" even with length one arg. pcfr2to2 <- pcfr[2] pcfr2to2a <- pcfr["USTotalIPI"] # same ## use "[[" or $ to get "PeriodicTS" pcfr2 <- pcfr[[2]] pcfr2a <- pcfr[["USTotalIPI"]] # same pcfr2b <- pcfr$USTotalIPI # same identical(pcfr2, pcfr2a) # TRUE identical(pcfr2, pcfr2b) # TRUE cycle(pcfr) frequency(pcfr)data(dataFranses1996) class(dataFranses1996) colnames(dataFranses1996) dim(dataFranses1996) # c(148, 19) plot(dataFranses1996[ , 2:11]) tipi <- dataFranses1996[ , "USTotalIPI"] plot(tipi) ## convert to PeriodicTS and remove NA's at the start and end pctipi <- pcts(tipi) pctipi <- window(pctipi, start = availStart(pctipi), end = availEnd(pctipi)) plot(pctipi) ## convert the whole dataset to class "PeriodicMTS" pcfr <- pcts(dataFranses1996) colnames(pcfr)[2:3] # "USTotalIPI" "CanadaUnemployment" ## subset as "PeriodicMTS" pcfr2to3 <- pcfr[2:3] plot(pcfr2to3) ## "[" "PeriodicMTS" even with length one arg. pcfr2to2 <- pcfr[2] pcfr2to2a <- pcfr["USTotalIPI"] # same ## use "[[" or $ to get "PeriodicTS" pcfr2 <- pcfr[[2]] pcfr2a <- pcfr[["USTotalIPI"]] # same pcfr2b <- pcfr$USTotalIPI # same identical(pcfr2, pcfr2a) # TRUE identical(pcfr2, pcfr2b) # TRUE cycle(pcfr) frequency(pcfr)
Replace methods for date in package pcts.
signature(x = "BasicCycle")signature(x = "Cyclic")ex1 is the autocorrelation function used in the reference as an
example when the solution of the periodic Yule-Walker system gives an
invalid PAR model. This can happen only if Lambert-Lacroix's
condition on the PAR order is not satisfied, see pdSafeParOrder.
A function of two arguments
See pp. 429–430 of the reference.
Lambert-Lacroix S (2005). “ Extension of autocovariance coefficients sequence for periodically correlated processes.” Journal of Time Series Analysis, 26(6), pp. 423-435.
data(ex1f) ## compute the first few autocorrelations pc3 <- slMatrix(period = 2, maxlag = 5, f = ex1f, type = "tt") ## Fir a PAR(0,2) model res0p2 <- alg1(pc3[],c(0,2)) ## model is invalid since a partial autocorrelation is larger than one: res0p2$be ## Find a modified order: pdSafeParOrder(c(0,2)) # PAR(1,2) ## now the parcor's are fine: res1p2 <- alg1(pc3[],c(1,2)) res1p2$bedata(ex1f) ## compute the first few autocorrelations pc3 <- slMatrix(period = 2, maxlag = 5, f = ex1f, type = "tt") ## Fir a PAR(0,2) model res0p2 <- alg1(pc3[],c(0,2)) ## model is invalid since a partial autocorrelation is larger than one: res0p2$be ## Find a modified order: pdSafeParOrder(c(0,2)) # PAR(1,2) ## now the parcor's are fine: res1p2 <- alg1(pc3[],c(1,2)) res1p2$be
Get the coefficients of a periodic filter.
filterCoef is a generic function to extract the coefficients of
periodic filters. Argument convention can be used to force a
particular convention for the signs. The description here is for the
methods defined in this package.
If convention is missing, the coefficient matrix is returned as
stored in the object. Otherwise, if convention is one of the
strings "BJ", "--" or "-", the coefficients
returned have the opposite sign of those in the auxilliary polynomial
(Box-Jenkins' convention). If convention is one of "SP",
"++" or "+", the coefficients are as in the auxilliary
polynomial (convention used in signal processing).
a matrix
signature(object = "PeriodicBJFilter", convention = "character")signature(object = "PeriodicSPFilter", convention = "character")filterCoef for further details;
PeriodicBJFilter for examples
Fit a subset PAR model with trigonometric parameterisation.
fit_trigPAR_optim(x, order, nseasons, seasonof1st = 1, maxiter = 200, harmonics = NULL, sintercept = FALSE, tol = 1e-07, type = c("vecbyrow", "bylag"), verbose = TRUE)fit_trigPAR_optim(x, order, nseasons, seasonof1st = 1, maxiter = 200, harmonics = NULL, sintercept = FALSE, tol = 1e-07, type = c("vecbyrow", "bylag"), verbose = TRUE)
x |
time series. |
order |
order, an integer number. |
nseasons |
number of seasons, an integer number. |
seasonof1st |
season of the first observation. |
maxiter |
max number of iterations. |
harmonics |
the harmonics to include in the model, vector of non-negative integers. |
sintercept |
if |
tol |
when to stop the iterations. |
type |
type of parameterisation, currently one of |
verbose |
if |
Fits a subset PAR model using trigonometric parameterisation, i.e. Fourier series for the periodic coefficients written in terms of sines and cosines.
If argument type is bylag, the parameters for each lag
are parameterised independently from other lags. If sintercept
is TRUE, it has its own trigonometric representation.
If argument type is vecbyrow (“Vec operation by
row”), the PAR parameters are stacked in a vector with all parameters
for the first season, followed by all parameters for the second, and
so on. The trigonometric parameterisation for this vector is used.
So the fundamental frequency is 1/(nseasons * order).
If sintercept is TRUE when type = vecbyrow, then
then the intercept for eaach season is put before the PAR parameters
and the fundamental frequency becomes 1/(nseasons * (order + 1).
Putting together the intercepts and the PAR parameters may not be very
useful for parsimonious trigonometric parameterisation, so to have a
separate set of coefficients for the intercepts set
attribute"merge" of sintercept to FALSE.
an object from class SubsetPM
This function may change.
Georgi N. Boshnakov
## see examples for class "SubsetPM"## see examples for class "SubsetPM"
Generic function with methods for fitting periodic time series models.
fitPM( model, x, ...)fitPM( model, x, ...)
x |
the time series. |
model |
a periodic model, see Details. |
... |
further arguments to be passed on to individual methods. |
This is a generic function.
model provides the specification of the model. In particular,
the class of model determines what model is fitted. Specific
values of the parameters are generally ignored by non-iterative
methods but some methods can handle more detailed specifications, see
the individual methods.
the fitted model,
typically an object of class class(model)
signature(model = "ANY", x = "ANY")This is the default method. It simply exits with an error message
stating that fitPM does not have a method for the model
specified by model.
signature(model = "numeric", x = "ANY")Fits a PAR model to x. model should be a vector of
non-negative integers giving the PAR order. The length of this vector
is taken to be the number of seasons.
This is a convenience method. It constructs a PAR model and callls the
method for model = "PeriodicArModel".
signature(model = "PeriodicArModel", x = "ANY")Fits a PAR model.
signature(model = "mcSpec", x = "ANY")Fits a periodic model according to the specification given by
model.
Currently this method uses mC.ss to set up the
optimisation environment and then calls one of the optimisation
functions in that environment as specified by argument
optim.method, see below.
Additional arguments may be specified to control the optimisation.
Argument init can be used to give initial values. It is
passed on to mC.ss (and so has the format required by it).
optim.method is the name of an optimisation function in the
environment returned by mC.ss. The default is
optim.method = "minim", which is based on the standard R function
optim. Alternatives are "minimBB" or "minimBBLU". All this
needs to be documented but see mC.ss and xx.ss for
details.
Further arguments are passed on to the optimisation method. A
typical argument supported by most optimisation functions is
control.
signature(model = "PiPeriodicArModel", x = "ANY")Fits a periodically integrated PAR model using the parameters of
model as initial values. Calls pclspiar to do the
actual work.
signature(model = "SiPeriodicArModel", x = "ANY")Fits a seasonally integrated PAR model.
signature(model = "PeriodicArModel", x = "PeriodicMTS")signature(model = "PeriodicArModel", x = "PeriodicTS")Georgi N. Boshnakov
(todo: to be completed properly later)
Hipel KW, McLeod AI (1994). Time series modelling of water resources and environmental systems, Developments in water science; 45. London; Amsterdam: Elsevier.
Boshnakov GN, Iqelan BM (2009). “Generation of time series models with given spectral properties.” J. Time Series Anal., 30(3), 349–368. ISSN 0143-9782, doi:10.1111/j.1467-9892.2009.00617.x.
## newm1 <- list(phi = matrix(1:12, nrow=4), p=rep(3,4), period=4, si2 = rep(1,4)) ## new_pfm1 <- PeriodicFilterModel(newm1, intercept=0) ## generate some data; set.seed(1234) simts1 <- pcts(rnorm(1024), nseasons = 4) fitPM(c(3,3,3,3), simts1) fitPM(3, simts1) ## the fit on the underlying data is equivalent. fitPM(c(3,3,3,3), as.numeric(simts1)) ## equivalently, use a PAR(3,3,3,3) model for argument 'model' ## here the coefficients of pfm1 are ignored, since the estimation is linear. pfm1 <- PeriodicArModel(matrix(1:12, nrow = 4), order = rep(3,4), sigma2 = 1) pfm1 ## these give same results as above fitPM(pfm1, simts1) fitPM(pfm1, as.numeric(simts1)) fitPM(c(1,1,1,1), simts1) fitPM(c(3,2,2,1), simts1) fitPM(c(3,2,2,2), simts1) pdSafeParOrder(c(3,2,2,1)) pdSafeParOrder(rev(c(3,2,2,1))) x <- arima.sim(list(ar = 0.9), n = 960) pcx <- pcts(x, nseasons = 4) mx <- matrix(x, nrow = 4) ##pc.acf(mx) ##pc.acf(mx, maxlag=10) ## TODO: avoid the warning when length ot the time series is not multiple autocovariances(t(mx), maxlag = 6, nseasons = 4) autocovariances(t(mx)) ##It is an error to have more columns than rows. ## autocovariances(mx, maxlag = 6, nseasons = 4) ## autocovariances(mx) num2pcpar(mx, c(1,1,1,1), period = 4) num2pcpar(mx, c(3,3,3,3), period = 4) sipfm1 <- new("SiPeriodicArModel", iorder = 1, siorder = 1, pcmodel = pfm1) sipfm1 fitPM(sipfm1, mx) pfm1 ## experiments and testing fit1 <- fitPM(c(3,3,3,3), simts1) fit1_mf <- new("MultiFilter", coef = fit1@ar@coef) vs <- mcompanion::mf_VSform(fit1_mf, form = "I") tmp <- mcompanion::VAR2pcfilter(vs$Phi[ , -4], Phi0inv = vs$Phi0inv, D = fit1@sigma2, what = "") names(tmp) # "pcfilter" "var" "Uform" tmp$var zapsmall(tmp$pcfilter) fit1@ar@coef all.equal(tmp$pcfilter[ , 1:3], fit1@ar@coef, check.attributes = FALSE) # TRUE tmp$Uform fit1@sigma2 ## both give the matrix Sigma for the "I" form identical( vs$Phi0inv %*% diag(fit1@sigma2) %*% t(vs$Phi0inv) , tmp$Uform$U0inv %*% diag(tmp$Uform$Sigma) %*% t(tmp$Uform$U0inv) ) # TRUE ## no, this is a different matrix var1_mat <- cbind(vs$Phi0, # identity matrix - vs$Phi) # drop trailing zero columns? var1_mat <- mcompanion::mCompanion(var1_mat) var1_Sigma <- vs$Phi0inv %*% diag(fit1@sigma2) %*% t(vs$Phi0inv) abs(eigen(diag(nrow(var1_mat)) - var1_mat)$values)## newm1 <- list(phi = matrix(1:12, nrow=4), p=rep(3,4), period=4, si2 = rep(1,4)) ## new_pfm1 <- PeriodicFilterModel(newm1, intercept=0) ## generate some data; set.seed(1234) simts1 <- pcts(rnorm(1024), nseasons = 4) fitPM(c(3,3,3,3), simts1) fitPM(3, simts1) ## the fit on the underlying data is equivalent. fitPM(c(3,3,3,3), as.numeric(simts1)) ## equivalently, use a PAR(3,3,3,3) model for argument 'model' ## here the coefficients of pfm1 are ignored, since the estimation is linear. pfm1 <- PeriodicArModel(matrix(1:12, nrow = 4), order = rep(3,4), sigma2 = 1) pfm1 ## these give same results as above fitPM(pfm1, simts1) fitPM(pfm1, as.numeric(simts1)) fitPM(c(1,1,1,1), simts1) fitPM(c(3,2,2,1), simts1) fitPM(c(3,2,2,2), simts1) pdSafeParOrder(c(3,2,2,1)) pdSafeParOrder(rev(c(3,2,2,1))) x <- arima.sim(list(ar = 0.9), n = 960) pcx <- pcts(x, nseasons = 4) mx <- matrix(x, nrow = 4) ##pc.acf(mx) ##pc.acf(mx, maxlag=10) ## TODO: avoid the warning when length ot the time series is not multiple autocovariances(t(mx), maxlag = 6, nseasons = 4) autocovariances(t(mx)) ##It is an error to have more columns than rows. ## autocovariances(mx, maxlag = 6, nseasons = 4) ## autocovariances(mx) num2pcpar(mx, c(1,1,1,1), period = 4) num2pcpar(mx, c(3,3,3,3), period = 4) sipfm1 <- new("SiPeriodicArModel", iorder = 1, siorder = 1, pcmodel = pfm1) sipfm1 fitPM(sipfm1, mx) pfm1 ## experiments and testing fit1 <- fitPM(c(3,3,3,3), simts1) fit1_mf <- new("MultiFilter", coef = fit1@ar@coef) vs <- mcompanion::mf_VSform(fit1_mf, form = "I") tmp <- mcompanion::VAR2pcfilter(vs$Phi[ , -4], Phi0inv = vs$Phi0inv, D = fit1@sigma2, what = "") names(tmp) # "pcfilter" "var" "Uform" tmp$var zapsmall(tmp$pcfilter) fit1@ar@coef all.equal(tmp$pcfilter[ , 1:3], fit1@ar@coef, check.attributes = FALSE) # TRUE tmp$Uform fit1@sigma2 ## both give the matrix Sigma for the "I" form identical( vs$Phi0inv %*% diag(fit1@sigma2) %*% t(vs$Phi0inv) , tmp$Uform$U0inv %*% diag(tmp$Uform$Sigma) %*% t(tmp$Uform$U0inv) ) # TRUE ## no, this is a different matrix var1_mat <- cbind(vs$Phi0, # identity matrix - vs$Phi) # drop trailing zero columns? var1_mat <- mcompanion::mCompanion(var1_mat) var1_Sigma <- vs$Phi0inv %*% diag(fit1@sigma2) %*% t(vs$Phi0inv) abs(eigen(diag(nrow(var1_mat)) - var1_mat)$values)
Class FittedPeriodicArmaModel in package pcts
Objects can be created by calls of the form new("FittedPeriodicArmaModel", ..., mean).
ar:Object of class "PeriodicBJFilter" ~~
ma:Object of class "PeriodicSPFilter" ~~
modelCycle:Object of class "BasicCycle" ~~
center:Object of class "numeric" ~~
intercept:Object of class "numeric" ~~
sigma2:Object of class "numeric" ~~
theTS:Object of class "PeriodicTS" ~~
asyCov:Object of class "ANY" ~~
ns:Object of class "numeric" ~~
Class "PeriodicArmaModel", directly.
Class "FittedPM", directly.
Class "VirtualPeriodicArmaModel", by class "PeriodicArmaModel", distance 2.
Class "PeriodicArmaSpec", by class "PeriodicArmaModel", distance 2.
Class "VirtualPeriodicFilterModel", by class "PeriodicArmaModel", distance 3.
Class "VirtualPeriodicStationaryModel", by class "PeriodicArmaModel", distance 3.
Class "PeriodicArmaFilter", by class "PeriodicArmaModel", distance 3.
Class "PeriodicInterceptSpec", by class "PeriodicArmaModel", distance 3.
Class "VirtualPeriodicAutocovarianceModel", by class "PeriodicArmaModel", distance 4.
Class "VirtualPeriodicMeanModel", by class "PeriodicArmaModel", distance 4.
Class "VirtualArmaFilter", by class "PeriodicArmaModel", distance 4.
Class "ModelCycleSpec", by class "PeriodicArmaModel", distance 4.
Class "InterceptSpec", by class "PeriodicArmaModel", distance 4.
Class "VirtualPeriodicModel", by class "PeriodicArmaModel", distance 5.
Class "VirtualMonicFilter", by class "PeriodicArmaModel", distance 5.
signature(object = "FittedPeriodicArmaModel"): ...
signature(object = "FittedPeriodicArmaModel"): ...
Class FittedPeriodicArModel.
Objects can be created by calls of the form new("FittedPeriodicArModel", ar, ma, sigma2, ...).
asyCov:Object of class "ANY" ~~
sigma2:Object of class "numeric" ~~
ar:Object of class "PeriodicArFilter" ~~
ma:Object of class "PeriodicMaFilter" ~~
center:Object of class "numeric" ~~
intercept:Object of class "numeric" ~~
theTS:Object of class "PeriodicTS" ~~
ns:Object of class "numeric" ~~
modelCycle:Object of class "BasicCycle" ~~
Class "PeriodicArModel", directly.
Class "PeriodicArmaModel", by class "PeriodicArModel", distance 2.
Class "VirtualPeriodicArmaModel", by class "PeriodicArModel", distance 3.
Class "PeriodicArmaSpec", by class "PeriodicArModel", distance 3.
Class "VirtualPeriodicFilterModel", by class "PeriodicArModel", distance 4.
Class "VirtualPeriodicStationaryModel", by class "PeriodicArModel", distance 4.
Class "VirtualPeriodicAutocovarianceModel", by class "PeriodicArModel", distance 5.
Class "VirtualPeriodicMeanModel", by class "PeriodicArModel", distance 5.
signature(object = "FittedPeriodicArModel"): ...
signature(object = "FittedPeriodicArModel"): ...
signature(object = "FittedPeriodicArModel"): ...
Data for four stocks since 2016-01-01.
data("four_stocks_since2016_01_01")data("four_stocks_since2016_01_01")
A list with components "DELL","MSFT", "INTC", "IBM".
Each component is a time series from class "xts" "zoo".
Stock market data for Dell, Microsoft, Intel and IBM, from 2016-01-01 to 2020-04-17. The Dell data start from 2016-08-17. All data were downloaded from Yahoo Finance on 2020-04-18.
https://finance.yahoo.com/
data(four_stocks_since2016_01_01) DELL <- four_stocks_since2016_01_01$DELL head(DELL) tail(DELL) dell <- pcts(DELL) head(as_datetime(dell)) head(Pctime(dell)) ## Weekends are totally absent from the data, ## so a Monday-Friday sub-cycle is created: nSeasons(dell) dell@cycle ## there are some NA's in the data, due to Bank holidays Pctime(c(2624, 5), pcCycle(dell)) # "W2624 Fri" as_datetime(Pctime(c(2624, 5), pcCycle(dell))) # "2020-04-10 UTC" ## dell["2020-04-10 UTC"] head(cycle(dell)) tail(Pctime(dell)) tail(as.Date(Pctime(dell)))data(four_stocks_since2016_01_01) DELL <- four_stocks_since2016_01_01$DELL head(DELL) tail(DELL) dell <- pcts(DELL) head(as_datetime(dell)) head(Pctime(dell)) ## Weekends are totally absent from the data, ## so a Monday-Friday sub-cycle is created: nSeasons(dell) dell@cycle ## there are some NA's in the data, due to Bank holidays Pctime(c(2624, 5), pcCycle(dell)) # "W2624 Fri" as_datetime(Pctime(c(2624, 5), pcCycle(dell))) # "2020-04-10 UTC" ## dell["2020-04-10 UTC"] head(cycle(dell)) tail(Pctime(dell)) tail(as.Date(Pctime(dell)))
Mean monthly flow (cms) of Fraser River From March 1912 to December 2017, recorded by Fraser River at Hope station.
data("Fraser2017")data("Fraser2017")
A time series (class "ts") with frequency 12, starting from
January 1912 (the first two data values are NA) to December 2017.
Dataset Fraser2017 is an extention of dataset "Fraser"
in package "pear". The latter runs upto December 1990 (not the
documented December 1991). At the time of writing this package
"pear" is archived on CRAN, which is the main reason to include
the dataset (with the added benefit of almost 30 years of additional
data).
dataFranses1996,
four_stocks_since2016_01_01
data(Fraser2017) fr <- window(Fraser2017, start = c(1912, 3), end = c(1990, 12)) ## all.equal(as.numeric(fr), as.numeric(pear::Fraser)) # TRUE ## all.equal(tsp(fr), tsp(pear::Fraser)) # TRUEdata(Fraser2017) fr <- window(Fraser2017, start = c(1912, 3), end = c(1990, 12)) ## all.equal(as.numeric(fr), as.numeric(pear::Fraser)) # TRUE ## all.equal(tsp(fr), tsp(pear::Fraser)) # TRUE
Methods for function maxLag() in package 'pcts'.
signature(object = "PeriodicArmaFilter")## non-periodic autocovariances maxLag(autocovariances(AirPassengers)) ## periodic pcts_exdata() # creates ap, ap7to9, pcfr, pcfr2to4, maxLag(autocovariances(ap, maxlag = 6)) ## pcarma filter m <- rbind(c(0.81, 0), c(0.4972376, 0.4972376)) ar_filt3 <- new("PeriodicBJFilter", coef = m, order = c(1,2)) arma_filt3 <- new("PeriodicArmaFilter", ar = ar_filt3) maxLag(arma_filt3)## non-periodic autocovariances maxLag(autocovariances(AirPassengers)) ## periodic pcts_exdata() # creates ap, ap7to9, pcfr, pcfr2to4, maxLag(autocovariances(ap, maxlag = 6)) ## pcarma filter m <- rbind(c(0.81, 0), c(0.4972376, 0.4972376)) ar_filt3 <- new("PeriodicBJFilter", coef = m, order = c(1,2)) arma_filt3 <- new("PeriodicArmaFilter", ar = ar_filt3) maxLag(arma_filt3)
Creates an environment for mc-fitting. These functions are transitory, hence the strange names.
mC.ss(spec, ...) xx.ss(period, type.eigval, n.root, eigabs, eigsign, co_r, co_arg, init = NULL, len.block = NULL, mo.col, generators = NULL)mC.ss(spec, ...) xx.ss(period, type.eigval, n.root, eigabs, eigsign, co_r, co_arg, init = NULL, len.block = NULL, mo.col, generators = NULL)
spec |
a model, an object of class mcSpec. |
... |
further arguments to be passed on to |
period |
the number of seasons. |
type.eigval |
types of the eigenvalues, a character vector with elements "r" or "cp", see Details. |
n.root |
number of roots. Currently the dimension of the matrix is set to this. |
eigabs |
The absolute values/moduli of the eigenvalues, numeric vector. |
eigsign |
The signs/moduli of the eigenvalues. |
co_r |
similar to |
co_arg |
similar to |
init |
initial values, see Details. |
len.block |
lengths of Jordan blocks. |
mo.col |
last non-zero column in the top of the matrix. |
generators |
~~ TODO: describe this argument. ~~ |
mC.ss takes the specification of the model as an object of
class mcSpec and calls xx.ss.
Basically, the value returned by these functions is an extended model specification together with an environment which can be used for fitting the model, exploring the results and trying various things. This may be used for getting better understanding of the model and the optimisation routines.
The result of both functions is a list, containing several functions
and an environment. The environment (element env) is the most
important element since it allows access to everything in the model
environment. The function elements of the list are simply a
convenience.
Several functions in env are available for fitting the
model. Currently these are minim, minimBB and
minimBBlu. The first argument of all these functions is a time
series to which the model is to be fitted. By default, a conditional
likelihood is being optimised. To base the optimisation on conditional
sum of squares, set argument CONDLIK to FALSE. The remaining
arguments in a call to any of the above functions are passed on to the
corresponding optimisation routine (whose help page should be
consulted for details).
minim uses the core R function optim.
minimBB and minimBBlu use BBoptim from package
BB. They result is a list, as returned by the corresponding
optimisation function with the optimal parameters in element
par. The elements of this vector are named to help somewhat in
its interpretation but complete information about the fitted model can
be obtained from the environment.
Firstly, at the end of the optimisation, the optimal parameters and
other information are stored in env. If the same call (maybe
with modified instructions for the optimisation) is repeated, these
parameters will be used as initial values for a new optimisation
run. This may be useful, for example, if the previous run didn't
converge.
Secondly, properties of the fitted model and more useful
representations can be obtained using functions in the environment or
the convinience functions in the list returned by xx.ss.
optparam2mcparam converts a vector of parameters into the
more familiar filter representation, where the i-th row contains the
coefficients for the i-th season. This function takes one argument the
vector of parameters, e.g. the one returned by the fitting
functions. It updates a number of variables in env, computes
the filter representation of the model and stores it in
wrkmodel. It returns NULL.
This function may be used for exploratory purposes or to set new
values for the parameters, e.g. to be used as starting values for a
new optimisation run.
mcparam2optparam does the opposite. It converts the current
model in env to a vector of parameter. This function does not
have arguments.
mclik computes the value of the conditional likelihood for
given parameters. Its first argument is a time series, the second is a
vector of parameters and the third is a vector of innovations. Only
the first argument is compulsory. If param is not supplied, the
current parameters in env are used. Otherwise, they are updated
with the new parameters and then used. The innovations default to the
zero vector.
mcss is similar but computes the conditional sum of squares.
Argument init can be used to provide initial
values. If it is missing or NULL, random initial values are generated
for the free parameters.
init may also be a numeric vector suitable for the call
optparam2mcparam(init), see above. This vector would typically
come from a previous optimisation run.
init may also be a list with elements "eigabs",
"eigsign", "co_r", "co_abs". These components
have the same meaning as the corresponding arguments of xx.ss.
TODO: more is needed here!
A list with the following components:
fmcss |
a function to compute the sum of squares for a model. |
fparamvec |
a function to convert mc-parameters to optimisation parameters. |
fmcparam |
a function to convert optimisation parameters to mc-parameters. |
env |
an object of class |
Georgi N. Boshnakov
Boshnakov GN, Iqelan BM (2009). “Generation of time series models with given spectral properties.” J. Time Series Anal., 30(3), 349–368. ISSN 0143-9782, doi:10.1111/j.1467-9892.2009.00617.x.
xx.ss which is called by mC.ss
# test0 roots spec.coz2 <- mcompanion::mcSpec(dim = 5, mo = 4, root1 = c(1,1), order = rep(2,4)) spec.coz2 xxcoz2a <- mC.ss(spec.coz2) ## test0 roots spec.coz4 <- mcompanion::mcSpec(dim = 5, mo = 4, root1 = c(1,1), order = rep(3,4)) xxcoz4a <- mC.ss(spec.coz4)# test0 roots spec.coz2 <- mcompanion::mcSpec(dim = 5, mo = 4, root1 = c(1,1), order = rep(2,4)) spec.coz2 xxcoz2a <- mC.ss(spec.coz2) ## test0 roots spec.coz4 <- mcompanion::mcSpec(dim = 5, mo = 4, root1 = c(1,1), order = rep(3,4)) xxcoz4a <- mC.ss(spec.coz4)
Asymptotic covariance matrix of periodic mean.
meanvarcheck(parmodel, n) meancovmat(parmodel, n, cor = FALSE, result = "var")meanvarcheck(parmodel, n) meancovmat(parmodel, n, cor = FALSE, result = "var")
parmodel |
a periodic model. |
n |
number of observations (TODO: need clarification here). |
cor |
if |
result |
if |
Computes asymptotic covariance or correlation matrix of the periodic means.
if result = "var" a matrix,
otherwise a vector
Georgi N. Boshnakov
x <- arima.sim(list(ar=0.9), n=1000) proba1 <- fitPM(c(3,2,2,2), x) meancovmat(proba1, 100) meancovmat(proba1, 100, cor = TRUE) meancovmat(proba1, 100, result = "") meancovmat(proba1, 100, cor = TRUE, result = "") meanvarcheck(proba1, 100)x <- arima.sim(list(ar=0.9), n=1000) proba1 <- fitPM(c(3,2,2,2), x) meancovmat(proba1, 100) meancovmat(proba1, 100, cor = TRUE) meancovmat(proba1, 100, result = "") meancovmat(proba1, 100, cor = TRUE, result = "") meanvarcheck(proba1, 100)
Get the cycle of a periodic object, a generic function.
modelCycle(object) modelCycle(object, ... ) <- valuemodelCycle(object) modelCycle(object, ... ) <- value
object |
an object. |
value |
the new value for the cycle, an object inheriting from
|
... |
not used. |
modelCycle is essentially internal, for programming. The user
level function to get the cycle of an object is pcCycle.
modelCycle returns the Cycle object (in the sense of package
pcts), associated with object. modelCycle is a
generic function which makes it possible to associate a cycle with
objects from a class, without inheriting from the cycle classes.
By definition, NULL represents the model cycle of objects from
classes with no (inherited) method for modelCycle.
The default method of modelCycle returns NULL.
The default method for its replacement version throws error.
for modelCycle, an object inheriting from class
"BasicCycle" or NULL;
"modelCycle<-" is used for the side effect of changing the
cycle of object.
signature(object = "ANY")signature(object = "ModelCycleSpec")Class ModelCycleSpec.
Objects can be created by calls of the form new("ModelCycleSpec", ...).
modelCycle:Object of class "BasicCycle" ~~
signature(object = "ModelCycleSpec"): ...
signature(object = "ModelCycleSpec"): ...
Basic information about periodic periodic time series objects.
nCycles(x, ...) nTicks(x) nVariables(x, ...) nSeasons(object)nCycles(x, ...) nTicks(x) nVariables(x, ...) nSeasons(object)
x, object
|
an object from a periodic time series class. |
... |
further arguments for methods. |
nTicks gives the number of time points, i.e. number of rows in
the matrix representation.
nVariables gives the number of variables in the time series.
nSeasons gives the number of seasons of time series and other
periodic objects.
nCycles gives the number of cycles available in the data,
e.g. number of years for monthly data. It always gives an integer
number. Currently, if the result is not an integer an error is
raised. TODO: There is a case to round up or give the number of full
cycles available but this seems somewhat dangerous if done quietly. A
good alternative is to provide argument for control of this.
There are further functions to get or set the names of the units of
season and the seasons, see allSeasons.
an integer number
Georgi N. Boshnakov
allSeasons, "nSeasons-methods"
ap <- pcts(AirPassengers) nVariables(ap) nTicks(ap) nCycles(ap) nSeasons(ap) monthplot(ap) boxplot(ap)ap <- pcts(AirPassengers) nVariables(ap) nTicks(ap) nCycles(ap) nSeasons(ap) monthplot(ap) boxplot(ap)
Number of seasons of a periodic object.
## S4 method for signature 'Cyclic' nSeasons(object) ## same signature for all periodic classes in package "pcts"## S4 method for signature 'Cyclic' nSeasons(object) ## same signature for all periodic classes in package "pcts"
object |
an object for which the notion of number of seasons makes sense. |
nSeasons is a generic function. This page gives is for the
methods defined in package "pcts" - all periodic classes have
(or inherit) a method.
an integer number
signature(object = "DayWeekCycle")signature(object = "MonthYearCycle")signature(object = "PeriodicIntegratedArmaSpec")signature(object = "QuarterYearCycle")signature(object = "PeriodicMonicFilterSpec")signature(object = "PeriodicInterceptSpec")signature(object = "Cyclic")signature(object = "BareCycle")signature(object = "OpenCloseCycle")signature(object = "Every30MinutesCycle")signature(object = "PartialCycle")signature(object = "VirtualPeriodicModel")signature(object = "SarimaFilter")signature(object = "VirtualArmaFilter")Georgi N. Boshnakov
allSeasons for other functions related to the
seasonality of an object;
nCycles for related functions
## scalar time series ap <- pcts(AirPassengers) nSeasons(ap) # 12 ## multivariate time series pcfr <- pcts(dataFranses1996) nSeasons(pcfr) # 4 ## five-day-week period five_day_week <- BuiltinCycle(5) five_day_week nSeasons(five_day_week)## scalar time series ap <- pcts(AirPassengers) nSeasons(ap) # 12 ## multivariate time series pcfr <- pcts(dataFranses1996) nSeasons(pcfr) # 4 ## five-day-week period five_day_week <- BuiltinCycle(5) five_day_week nSeasons(five_day_week)
Fit PAR model using sample autocorrelations.
num2pcpar(x, order, result = NULL, ...)num2pcpar(x, order, result = NULL, ...)
x |
time series, a numeric vector. |
order |
PAR order, a single number or a vector with one entry for each season. |
result |
what to return, the default is to return the full model, see Details. |
... |
passed on to |
Computes the periodic autocorrelations and fits a PAR model using the Periodic Levinson-Durbin algorithm.
The order is a vector of non-negative integers, specifying the
autoregressive orders for each season. If order is a single
number, then all seasons have that order.
mean controls centering in the computation of the
autocorrelations. If mean is numeric, then subtract the
supplied mean before computing the autocovariances. If mean is
TRUE, the default, compute and subtract the sample periodic mean
before computing the autocovariances. If mean is FALSE, do not
centre the series, i.e. assume that the mean is zero.
If result is NULL, the default, returns the full model. If
result = "coef", returns the PAR coefficients only (currently
any value of result other than NULL has this effect).
The coefficients of the fitted model or a list with components:
mean |
the mean, set as described in Details. |
coef |
forward prediction coefficients. |
scale |
standard deviations of the innovations. |
Georgi N. Boshnakov
fitPM which uses num2pcpar for calculations
## Not run: simts1 <- matrix(rnorm(100), nrow = 4) num2pcpar(simts1, order = c(3,2,2,2), period = 4 ) num2pcpar(simts1, order = c(3,2,1,2), period = 4 ) pdSafeParOrder(c(3,2,1,2)) pdSafeParOrder(c(3,2,2,1)) num2pcpar(simts1, order = c(3,2,2,1), period = 4 ) num2pcpar(simts1, order = pdSafeParOrder(c(3,2,2,1)), period = 4 ) num2pcpar(simts1, order = c(3,2,1,2), period = 4 ) num2pcpar(simts1, order = c(3,2,1,2), period = 4, mean = rep(0,4) ) num2pcpar(simts1, order = c(3,2,1,2), period = 4, mean = FALSE ) num2pcpar(simts1, order = c(3,2,1,2), period = 4, mean = FALSE )$coef@m - num2pcpar(simts1, order = c(3,2,1,2), period = 4 )$coef@m ## End(Not run)## Not run: simts1 <- matrix(rnorm(100), nrow = 4) num2pcpar(simts1, order = c(3,2,2,2), period = 4 ) num2pcpar(simts1, order = c(3,2,1,2), period = 4 ) pdSafeParOrder(c(3,2,1,2)) pdSafeParOrder(c(3,2,2,1)) num2pcpar(simts1, order = c(3,2,2,1), period = 4 ) num2pcpar(simts1, order = pdSafeParOrder(c(3,2,2,1)), period = 4 ) num2pcpar(simts1, order = c(3,2,1,2), period = 4 ) num2pcpar(simts1, order = c(3,2,1,2), period = 4, mean = rep(0,4) ) num2pcpar(simts1, order = c(3,2,1,2), period = 4, mean = FALSE ) num2pcpar(simts1, order = c(3,2,1,2), period = 4, mean = FALSE )$coef@m - num2pcpar(simts1, order = c(3,2,1,2), period = 4 )$coef@m ## End(Not run)
Compute asymptotic covariance matrix for PAR model
parcovmatlist(parmodel, n, cor = FALSE, result = "list")parcovmatlist(parmodel, n, cor = FALSE, result = "list")
parmodel |
PAR model, object of class |
n |
length of the series or a vector with one element for each season. |
cor |
If TRUE return correlation matrix. |
result |
if "list", the default, return a list, if "Matrix" return a Matrix object, otherwise return an ordinary matrix, see Details. |
Uses eq. (3.3) in the reference.
If result = "list", parcovmatlist returns a list whose
s-th element is the covariance matrix of the PAR parameters for the
s-th season. Otherwise, if result = "Matrix" it returns a
block-diagonal matrix created by .bdiag() from package
"Matrix". If result = "matrix" it returns an ordinary matrix
(with the current implementation this is returned for any value other
than "list" or "Matriix").
a list, matrix or block-diagonal matrix, as described in Details
Georgi N. Boshnakov
McLeod AI (1994). “Diagnostic checking of periodic autoregression models with application.” Journal of Time Series Analysis, 15(2), 221–233.
x <- arima.sim(list(ar=0.9), n=1000) proba1 <- fitPM(c(3,2,2,2), x) parcovmatlist(proba1, 100) parcovmatlist(proba1, 100, cor = TRUE) sqrt(diag(parcovmatlist(proba1, 100, cor = TRUE)[[1]])) meanvarcheck(proba1, 100)x <- arima.sim(list(ar=0.9), n=1000) proba1 <- fitPM(c(3,2,2,2), x) parcovmatlist(proba1, 100) parcovmatlist(proba1, 100, cor = TRUE) sqrt(diag(parcovmatlist(proba1, 100, cor = TRUE)[[1]])) meanvarcheck(proba1, 100)
Methods for computation of periodic partial autocorrelations.
signature(x = "PeriodicAutocovariances", maxlag = "ANY", lag_0 = "missing")signature(x = "VirtualPeriodicAutocovariances", maxlag = "ANY", lag_0 = "ANY")partialAutocorrelations in package sarima
for further details.
partialVariances,
partialAutocovariances
Compute periodic partial autocovariances.
signature(x = "VirtualPeriodicAutocovariances")partialAutocorrelations in package sarima
for further details.
partialAutocorrelations,
partialVariances
Methods for computation of periodic partial coefficients.
signature(x = "PeriodicArModel")signature(x = "VirtualPeriodicAutocovariances")Class PartialCycle
Objects can be created by calls of the form new("PartialCycle", ...).
Partial cycles are often created implicitly when subsetting time series
using window() with argument seasons, see the examples.
orig:the parent class of the partial cycle, an object inheriting from
class "BasicCycle".
subindex:an integer vector specifying the seasons to include in the partial cycle.
Class "BasicCycle", directly.
signature(x = "PartialCycle", abb = "logical"): ...
signature(x = "PartialCycle", abb = "missing"): ...
signature(object = "PartialCycle"): ...
signature(x = "PartialCycle"): ...
signature(x = "PartialCycle"): ...
signature(object = "PartialCycle"): ...
dwc <- new("DayWeekCycle") dwc allSeasons(dwc) ## a five day week cycle dwc5 <- new("PartialCycle", orig = dwc, subindex = 1:5) dwc5 allSeasons(dwc5) weekend <- new("PartialCycle", orig = dwc, subindex = 6:7) weekend allSeasons(weekend) ap <- pcts(AirPassengers) ## take data for the summer months (in Northern hemisphere) ap7to9 <- window(ap, seasons = 7:9) ## the above implicitly creates a partial cycle ap7to9 allSeasons(ap7to9)dwc <- new("DayWeekCycle") dwc allSeasons(dwc) ## a five day week cycle dwc5 <- new("PartialCycle", orig = dwc, subindex = 1:5) dwc5 allSeasons(dwc5) weekend <- new("PartialCycle", orig = dwc, subindex = 6:7) weekend allSeasons(weekend) ap <- pcts(AirPassengers) ## take data for the summer months (in Northern hemisphere) ap7to9 <- window(ap, seasons = 7:9) ## the above implicitly creates a partial cycle ap7to9 allSeasons(ap7to9)
Class PartialPeriodicAutocorrelations.
Objects can be created by calls of the form new("PartialPeriodicAutocorrelations", ..., data).
modelCycle:Object of class "BasicCycle" ~~
data:Object of class "Lagged" ~~
Class "ModelCycleSpec", directly.
Class "FlexibleLagged", directly.
Class "VirtualPeriodicAutocorrelations", directly.
Class "Lagged", by class "FlexibleLagged", distance 2.
Class "VirtualPeriodicModel", by class "VirtualPeriodicAutocorrelations", distance 2.
signature(object = "PartialPeriodicAutocorrelations"): ...
Compute periodic partial variances.
signature(x = "VirtualPeriodicAutocovariances")partialVariances in package sarima
for further details.
partialAutocorrelations for for partial autocorrelations.
Compute a matrix of factors such that elementwise division of the periodic autocovariance matrix by it will give the periodic autocorrelations.
pc_sdfactor(sd, maxlag)pc_sdfactor(sd, maxlag)
sd |
standard deviations of the seasons numeric. |
maxlag |
maximal lag, a number. |
a matrix of coefficients of size period x (maxlag+1). The
length of sd is taken to be the period.
Georgi N. Boshnakov
## equivalent to data(Fraser, package = "pear") Fraser <- window(Fraser2017, start = c(1912, 3), end = c(1990, 12)) logfraser <- window(pcts(log(Fraser)), start = c(1913, 1)) acvf1 <- autocovariances(logfraser, maxlag = 2) fac <- pc_sdfactor(sqrt(acvf1[ , 0]), 2) fac[ , 1:3] acrf1 <- autocorrelations(logfraser, maxlag = 2) all.equal(acvf1[], acrf1[] * fac) # TRUE## equivalent to data(Fraser, package = "pear") Fraser <- window(Fraser2017, start = c(1912, 3), end = c(1990, 12)) logfraser <- window(pcts(log(Fraser)), start = c(1913, 1)) acvf1 <- autocovariances(logfraser, maxlag = 2) fac <- pc_sdfactor(sqrt(acvf1[ , 0]), 2) fac[ , 1:3] acrf1 <- autocorrelations(logfraser, maxlag = 2) all.equal(acvf1[], acrf1[] * fac) # TRUE
Filter time series with a periodic arma filter.
If whiten is FALSE (default) the function applies
the given ARMA filter to eps (eps is often periodic
white noise). If whiten is TRUE the function applies
the “inverse filter” to , effectively computing
residuals.
pc.filter(model, x, eps, seasonof1st = 1, from = NA, whiten = FALSE, nmean = NULL, nintercept = NULL)pc.filter(model, x, eps, seasonof1st = 1, from = NA, whiten = FALSE, nmean = NULL, nintercept = NULL)
x |
the time series to be filtered, a vector. |
eps |
residuals, a vector or NULL. |
model |
the model parameters, a list with components |
seasonof1st |
the season of the first observation (i.e., of x[1]). |
from |
the index from which to start filtering. |
whiten |
if TRUE use |
nmean |
a vector of means having the length of the series, see Details. |
nintercept |
a vector of intercepts having the length of the series, see details. |
The model is specified by argument model, which is a list with
the following components:
phithe autoregression parameters,
thetathe moving average parameters,
pthe autoregression orders, a single number or a vector with one element for each season,
qthe moving average orders, a single number or a vector with one element for each season,
periodnumber of seasons in a cycle,
meanmeans of the seasons,
interceptintercepts of the seasons.
The relation between x and eps is assumed to be the
following. Let
be the mean corrected series, where is the mean, see below.
The equation relating the
mean corrected series, , and
eps is the following:
where is the intercept, nintercept. The inverse
filter is obtained by writing this as an equation expressing
through the remaining quantities.
If whiten = TRUE, pc.filter uses the above formula to
compute the filtered values of x for t=from,...,n,
i.e. whitening the time series if eps is white noise. If
whiten = FALSE, eps is computed, i.e. the inverse filter
is applied x from eps, i.e. “colouring” x.
In both cases the first few values in x and/or eps are
used as initial values.
Essentially, the mean is subtracted from the series to obtain the
mean-corrected series, say y. Then either y is filtered
to obtain eps or the inverse filter is applied to obtain
y from eps
finally the mean is added back to y and the result returned.
The mean is formed by model$mean and argument nmean. If
model$mean is supplied it is recycled periodically to the
length of the series x and subtracted from x. If
argument nmean is supplied, it is subtracted from x. If
both model$mean and nmean are supplied their sum is
subtracted from x.
The above gives a vector y, , which is then filtered. If the mean is
zero, in the formulas below.
Finally, the mean is added back, , and the new
x is returned.
The above gives a vector y which is used in the filtering. If
the mean is zero, in the formulae below.
pc.filter can be used to simulate pc-arma series with the
default value of whiten=FALSE. In this case eps is the
input series and y the output.
Then model$mean or nmean are added to y to form the
output vector x.
Residuals corresponding to a series y can be obtained by
setting whiten=TRUE. In this case y is the input series.
The elements of the output vector eps are calculated by the
formula:
There is no need in this case to restore x since eps is
returned.
In both cases any necessary initial values are assumed to be already
in the vectors. If from is not supplied it is chosen as the
smallest i such that for all ,
t-p[t]>0 and t-q[t]>0, i.e. the filter will not require
negative indices for x or eps.
pc.filter calls the lower level function pc.filter.xarma
to do the computation.
The filtered series: the modified x if whiten=FALSE, the
modified eps if whiten=TRUE.
1
Georgi N. Boshnakov
the lower level functions
pc.filter.xarma
which do the computations
Filter time series with periodic arma filters with or options for periodic and non-periodic intercepts.
pc.filter.xarma(x, eps, phi, theta, period, p, q, n, from, seasonof1st = 1, intercept = NULL, nintercept = NULL)pc.filter.xarma(x, eps, phi, theta, period, p, q, n, from, seasonof1st = 1, intercept = NULL, nintercept = NULL)
x |
the time series to be filtered, a vector. |
eps |
the innovations, a vector. |
phi |
the autoregression parameters, a matrix. |
theta |
the moving average parameters, a matrix. |
period |
the period (number of seasons in a year). |
p |
the autoregression orders, recycled to |
q |
the moving average orders, recycled to |
n |
a positive integer, the time index of the last observation to be filtered. |
from |
a positive integer, the time index of the first observation to be filtered. |
seasonof1st |
a positive integer, the season of the time index of |
intercept |
the intercepts of the seasons, a vector of length |
nintercept |
intercepts, a vector of the same length as |
pc.filter.xarma is somewhat lower level.
The user level function is pc.filter which uses
pc.filter.xarma to do the computations.
pc.filter.xarma filters the time series x by the
following formula (for t=from,...,n):
where is the overall intercept at time , see
below. Values of x[t] for t outside the range
from,n, if any, are left unchanged. Values for t<from
are used as initial values when needed.
Two intercepts are provided for convenience and some flexibility. The
periodic intercept, intercept, is a vector of length
period. It is replicated to length n, taking care to
ensure that the first element of the resulting vector, say ,
starts with intercept[seasonof1st]. nintercept can be
an arbitrary vector of length n. It can be used to represent
trend or contributions from covariates. nintercept is not
necessarilly periodic and argument seasonof1st does not affect
its use. The overall intercept is obtained as the sum c = a +
nintercept.
Usually x is a numeric vector but it can also be a matrix in
which each column represents the data for one “year”.
Also, the length of x is typically, but not necessarilly, equal
to n. It is prudent to ensure that length(x) >= n and
this must be done if x is a matrix.
Argument phi is ignored if p==0,
argument theta is ignored if q==0.
pc.filter.xarma is meant to be called by other functions whose
task is to prepare the arguments with proper checks. It does not make
much sense to repeat the checks in pc.filter.xarma. In
particular, no check is made to ensure that from and n
are correctly specified.
This is a low level function meant to be used with basic vectors
and matrices. TODO: Implement in C/C++. In the current
implementation. it accesses the elements of the arguments with
straightforward indexing, so objects from classes may be used as
well, provided that x[t], eps[t], phi[t,i],
theta[t,i], as well as assignment to x[t], are defined
for scalar indices.
Returns x with x[from] to x[n] filled with the
filtered values and values outside the interval from,...,n
left unchanged.
The mode of x is left unchanged. In particular, x may be
a matrix with each row representing the data for a season. This is
convenient since periodic time series are often more easily processed
in this form.
0 (base)
Georgi N. Boshnakov
The h coefficients are scaled cross-covariances between the time series and the innovations. This function computes estimates for h using as input the observed series, a series of estimated innovations, and an estimate of the variance of the innovations.
pc.hat.h(x, eps, maxlag, si2hat)pc.hat.h(x, eps, maxlag, si2hat)
x |
the observed time series x(t) |
eps |
a series of esimated innovations |
maxlag |
maximum lag |
si2hat |
estimate of the variance of the innovations |
If missing, the variance of the innovations is estimated from eps.
A matrix of the coefficient up to lag maxlag with one row for each season.
Georgi N. Boshnakov
Boshnakov GN (1996). “Recursive computation of the parameters of periodic autoregressive moving-average processes.” J. Time Ser. Anal., 17(4), 333–349. ISSN 0143-9782, doi:10.1111/j.1467-9892.1996.tb00281.x.
Computes the variances of sample periodic autocorrelations from periodic white noise.
pcacf_pwn_var(nepoch, period, lag, season)pcacf_pwn_var(nepoch, period, lag, season)
lag |
desired lags, a vector of positive integers. |
season |
desired seasons. |
nepoch |
number of epochs. |
period |
number of seasons. |
These are given by McLeod (1994), see the reference, eq. (4.3).
A matrix whose (i,j)th entry contains the variance of the
autocorrelation coefficient for season season[i] and lag lag[j].
Georgi N. Boshnakov
McLeod AI (1994). “Diagnostic checking of periodic autoregression models with application.” Journal of Time Series Analysis, 15(2), 221–233.
pcacf_pwn_var(79, 12, 0:16, 1:12)pcacf_pwn_var(79, 12, 0:16, 1:12)
Compute PAR autocovariance matrix
pc.acf.parModel(parmodel, maxlag = NULL) pcacfMat(parmodel)pc.acf.parModel(parmodel, maxlag = NULL) pcacfMat(parmodel)
parmodel |
PAR model, an object of class |
maxlag |
maximum lag |
pc.acf.parModel returns the autocovariances of a PAR model in
season-lag form with maximum lag equal to maxlag. If
maxlag is larger than the available precomputed
autocovariances, they missing ones are computed using the Yule-Walker
relations. Note that pc.acf.parModel
assumes that there are enough precomputed autocovariances to use the
Yule-Walker recursions directly.
TODO: pc.acf.parModel is tied to the old classes since it accesses
their slots. Could be used as a template to streamline the method for
autocovariances for class "PeriodicAutocovariance".
The season-lag form can be easily converted to other forms with the
powerful indexing operator, see the examples and slMatrix-class.
pcacfMat is a convenience function for statistical
inference. It creates a covariance matrix with dimension chosen
automatically. This covariance matrix is such that the asymptotic
covariance matrix of the estimated parameters can be obtained by dividing
sub-blocks by innovation variances and inverting them. See,
eq. (3.3) in the reference.
for pcacfMat, a matrix
for pc.acf.parModel, an slMatrix
Georgi N. Boshnakov
McLeod AI (1994). “Diagnostic checking of periodic autoregression models with application.” Journal of Time Series Analysis, 15(2), 221–233.
x <- arima.sim(list(ar = 0.9), n = 1000) proba1 <- fitPM(c(3,2,2,2), x) acfb <- pc.acf.parModel(proba1, maxlag = 8) acfb[4:(-2), 4:(-2), type = "tt"] pcacfMat(proba1)x <- arima.sim(list(ar = 0.9), n = 1000) proba1 <- fitPM(c(3,2,2,2), x) acfb <- pc.acf.parModel(proba1, maxlag = 8) acfb[4:(-2), 4:(-2), type = "tt"] pcacfMat(proba1)
Calculate partial periodic autocorrelations, forward and backward prediction coefficients and error variances using the periodic Levinson-Durbin algorithm.
alg1(r, p)alg1(r, p)
r |
periodic autocovariances, a matrix, see ‘Details’. |
p |
autoregressive orders, numeric vector. |
alg1(r,p) calculates the partial periodic correlations from
autocovariances r and autoregression orders p. The
matrix r has the same format as that of the r slot of
pcAcvf objects. The periodicity, d, is set equal to
the number of rows in r. If the length of p is not
equal to the periodicity, all autoregressive orders are set to the
first element of p. This last feature is really meant to be
used only with a scalar p.
The convention for the signs of the coefficients is the one from Boshnakov(1996) and is consistent with other R time series functions.
pmax below stands for the maximal element of p,
i.e. the maximal AR order.
As in the non-periodic case, the periodic Levinson-Durbin algorithm
fits recursively models of order 0, 1, ..., pmax. Namely, at
step i the AR orders for all seasons are set to
i. This is done in a way that correctly handles the case when
not all elements of p are equal, see the references.
The essential quantities calculated by the periodic Levinson-Durbin
algorithm are returned as matrices, whose th rows
contain values for season . The complete details depend on
the quantities, as described below.
The partial autocorrelations, the forward innovation variances and
the backward innovation variances are returned as matrices with
d rows and 1+pmax columns, whose j-th columns contain
the quantities for order j-1 (partial autocorrelations, forward
innovation variances and backward innovation variances, respectively).
Note that the lag-0 partial autocorrelations are the autocovariances
for lag 0, see the references for details.
The forward autoregression parameters are returned as a list whose
th element is a matrix containing the coefficients for
order . Similarly for the backward autoregression parameters.
One often is interested in the model of order p only. Its
coefficients are given by af[[pmax]], while the innovation
variances are in the last column of fv.
A list with the following elements.
orders |
autoregression orders |
be |
partial autocorrelations, a matrix with d rows |
fv |
forward innovation variances, a matrix with d rows |
bv |
backward innovation variances, a matrix with d rows |
af |
forward autoregression parameters, a list with one element for the parameters for each order. |
ab |
backward autoregression parameters, a list with one element for the parameters for each order. |
The autoregression orders of the output are not necessarilly the same as those specified in the call. There may be no PAR model with the requested orders, see the references.
Georgi N. Boshnakov
Boshnakov GN (1996). “Recursive computation of the parameters of periodic autoregressive moving-average processes.” J. Time Ser. Anal., 17(4), 333–349. ISSN 0143-9782, doi:10.1111/j.1467-9892.1996.tb00281.x.
Lambert-Lacroix S (2000). “On periodic autoregressive process estimation.” IEEE Transactions on Signal Processing, 48(6), 1800-1803.
Lambert-Lacroix S (2005). “Extension of autocovariance coefficients sequence for periodically correlated processes.” Journal of Time Series Analysis, 26(3), 423-435.
r1 <- rbind(c(1,0.81,0.729),c(1,0.90,0.900)) alg1(r1,2) ## pc2 <- pcAcvf(init=r1) ## pc2a <- pcAcvf(init=r1,seasonnames=c("am","pm"), periodunit="day") # example of Lambert-Lacroix data(ex1f) pc3 <- slMatrix(period=2,maxlag=5,f=ex1f,type="tt") res0p2 <- alg1(pc3[],c(0,2)) res1p2 <- alg1(pc3[],c(1,2)) res3p3 <- alg1(pc3[],c(3,3)) paramsys1 <- pcarma_param_system(pc3, NULL, NULL, 2, 0, 2) t1 <- solve(paramsys1$A,paramsys1$b) # this is from tests.r but I have lost t1 # set it to pc3 below # note: t1 is not the t1 computed above and in other examples! t1 <- pc3 t1 t1[] alg1(t1[],c(1,1)) alg1(t1[],c(1,0)) alg1(t1[],c(0,1)) alg1(t1[],c(5,5)) alg1(t1[],c(2,2)) alg1(t1[],c(2,3)) alg1(t1[],c(3,3)) alg1(t1[],c(4,4)) alg1(t1[],c(5,5))r1 <- rbind(c(1,0.81,0.729),c(1,0.90,0.900)) alg1(r1,2) ## pc2 <- pcAcvf(init=r1) ## pc2a <- pcAcvf(init=r1,seasonnames=c("am","pm"), periodunit="day") # example of Lambert-Lacroix data(ex1f) pc3 <- slMatrix(period=2,maxlag=5,f=ex1f,type="tt") res0p2 <- alg1(pc3[],c(0,2)) res1p2 <- alg1(pc3[],c(1,2)) res3p3 <- alg1(pc3[],c(3,3)) paramsys1 <- pcarma_param_system(pc3, NULL, NULL, 2, 0, 2) t1 <- solve(paramsys1$A,paramsys1$b) # this is from tests.r but I have lost t1 # set it to pc3 below # note: t1 is not the t1 computed above and in other examples! t1 <- pc3 t1 t1[] alg1(t1[],c(1,1)) alg1(t1[],c(1,0)) alg1(t1[],c(0,1)) alg1(t1[],c(5,5)) alg1(t1[],c(2,2)) alg1(t1[],c(2,3)) alg1(t1[],c(3,3)) alg1(t1[],c(4,4)) alg1(t1[],c(5,5))
Give partial periodic autocorrelations or other partial prediction quantities for a pcAcvf object.
alg1util(x, s, at0 = 1)alg1util(x, s, at0 = 1)
x |
an object of a class inheriting from
|
s |
the required quantity, the name of one of the elements of
the list returned by |
at0 |
if not identical to "var", replace the elements of the result at lag zero with 1, see ‘Details’. |
This function is a wrapper for alg1(). It calls alg1, to
do the computations and returns the requested element as an object
from class slMatrix. The model order is set to the maximal lag
avialable in x,
If at0 is the character string "var", then the lag zero values
in the result are set to the lag zero autocovariances, otherwise they
are set to 1.
This is mainly relevant for the periodic partial autocorrelations
(s="be"), since the setting at0="var" ensures that they
are in one to one correspondence with the autocovariances.
the requested quantity as an object of type slMatrix
Georgi N. Boshnakov
Lambert-Lacroix S (2000). “On periodic autoregressive process estimation .” IEEE Transactions on Signal Processing, 48( 6 ), pp. 1800-1803.
Lambert-Lacroix S (2005). “ Extension of autocovariance coefficients sequence for periodically correlated processes.” Journal of Time Series Analysis, 26(6), pp. 423-435.
r1 <- rbind(c(1,0.81,0.729),c(1,0.90,0.900)) # example of Lambert-Lacroix data(ex1f) pc3 <- slMatrix(period=2,maxlag=5,f=ex1f,type="tt") res0p2 <- alg1(pc3[],c(0,2)) res1p2 <- alg1(pc3[],c(1,2)) res3p3 <- alg1(pc3[],c(3,3))r1 <- rbind(c(1,0.81,0.729),c(1,0.90,0.900)) # example of Lambert-Lacroix data(ex1f) pc3 <- slMatrix(period=2,maxlag=5,f=ex1f,type="tt") res0p2 <- alg1(pc3[],c(0,2)) res1p2 <- alg1(pc3[],c(1,2)) res3p3 <- alg1(pc3[],c(3,3))
Apply a function to each season.
pcApply(object, ...) ## S4 method for signature 'numeric' pcApply(object, nseasons, FUN, ...) ## S4 method for signature 'matrix' pcApply(object, nseasons, FUN, ...) ## S4 method for signature 'PeriodicTS' pcApply(object, FUN, ...) ## S4 method for signature 'PeriodicMTS' pcApply(object, FUN, ...)pcApply(object, ...) ## S4 method for signature 'numeric' pcApply(object, nseasons, FUN, ...) ## S4 method for signature 'matrix' pcApply(object, nseasons, FUN, ...) ## S4 method for signature 'PeriodicTS' pcApply(object, FUN, ...) ## S4 method for signature 'PeriodicMTS' pcApply(object, FUN, ...)
object |
an object for which periodic mean makes sense. |
nseasons |
number of seasons. |
FUN |
a function, as for |
... |
further arguments for |
For univariate periodic time series, pcApply applies FUN
to the data for each season. For multivariate periodic time series,
this is done for each variable.
The methods for "numeric" and "matrix" are equivalent to
those for "PeriodicTS" and "PeriodicMTS",
respectively. The difference is that the latter two don't need
argument nseasons and take the names of the seasons from
object.
Argument "..." is for further arguments to FUN. In
particular, with many standard R functions argument na.rm =
TRUE can be used to omit NA's, see the examples.
In the univariate case, when length(object) is an integer
multiple of the number of seasons the periodic mean is equivalent to
apply(matrix(object, nrow = nseasons), 1, FUN, ...).
numeric or matrix for the methods described here, see section Details.
signature(object = "matrix")signature(object = "numeric")signature(object = "PeriodicMTS")signature(object = "PeriodicTS")Georgi N. Boshnakov
pcApply(pcts(presidents), mean, na.rm = TRUE) pcMean(pcts(presidents), na.rm = TRUE) # same pcApply(pcts(presidents), median, na.rm = TRUE) pcApply(pcts(presidents), var, na.rm = TRUE) pcApply(pcts(presidents), sd, na.rm = TRUE) pcfr2to4 <- pcts(dataFranses1996)[2:4] pcApply(pcfr2to4, median, na.rm = TRUE) pcApply(pcfr2to4, sd, na.rm = TRUE)pcApply(pcts(presidents), mean, na.rm = TRUE) pcMean(pcts(presidents), na.rm = TRUE) # same pcApply(pcts(presidents), median, na.rm = TRUE) pcApply(pcts(presidents), var, na.rm = TRUE) pcApply(pcts(presidents), sd, na.rm = TRUE) pcfr2to4 <- pcts(dataFranses1996)[2:4] pcApply(pcfr2to4, median, na.rm = TRUE) pcApply(pcfr2to4, sd, na.rm = TRUE)
Compute the sum of squares for a given PAR model.
pcAr.ss(x, model, eps = numeric(length(x)))pcAr.ss(x, model, eps = numeric(length(x)))
x |
time series, a numeric vector. |
model |
a model. |
eps |
residuals, defaults to a vector of zeroes. This may be used for models with moving average terms, for example. |
todo:
a number
Georgi N. Boshnakov
Compute periodic autocorrelations from PAR coefficients. This effectively solves the inverse problem to that solved by the periodic Levinson-Durbin algorithm but does not use a recursion.
pcAR2acf(coef, sigma2, p, maxlag = 10)pcAR2acf(coef, sigma2, p, maxlag = 10)
coef |
PAR coefficients, a matrix, see Details. |
sigma2 |
innovations variances. |
p |
PAR order. |
maxlag |
How many lags to compute. |
coef is a matrix with the coefficients for season i in
the i-th row. The coefficients start from lag 1.
The first few autocorrelations are computed by solving a linear system, see the references. The rest, are generated using the periodic Yule-Walker equations.
a matrix, in which row s contains the acf's for season s
for lags 0, 1, ..., maxlag (in this order).
Georgi N. Boshnakov
Boshnakov GN (1996). “Recursive computation of the parameters of periodic autoregressive moving-average processes.” J. Time Ser. Anal., 17(4), 333–349. ISSN 0143-9782, doi:10.1111/j.1467-9892.1996.tb00281.x.
Boshnakov GN, Boteva A (1992). “An algorithm for the computation of the theoretical autocovariances of a periodic autoregression process.” Varna.
pcarma_acvf_lazy, which does the main computation, but note
that the coefficients for it start from lag zero
m <- rbind( c(0.81, 0), c(0.4972376, 0.4972376) ) si2 <- PeriodicVector(c(0.3439000, 0.1049724)) pcAR2acf(m) pcAR2acf(m, si2) pcAR2acf(m, si2, 2) pcAR2acf(m, si2, 2, maxlag = 10) # same using pcarma_acvf_lazy directly m1 <- rbind( c(1, 0.81, 0), c(1, 0.4972376, 0.4972376) ) testphi <- slMatrix(init = m1) myf <- pcarma_acvf_lazy(testphi, testtheta, si2, 2, 0, 2, maxlag = 10) myf(1:2, 0:9) # get a matrix of values all(myf(1:2, 0:9) == pcAR2acf(m, si2, 2, maxlag = 9)) # TRUEm <- rbind( c(0.81, 0), c(0.4972376, 0.4972376) ) si2 <- PeriodicVector(c(0.3439000, 0.1049724)) pcAR2acf(m) pcAR2acf(m, si2) pcAR2acf(m, si2, 2) pcAR2acf(m, si2, 2, maxlag = 10) # same using pcarma_acvf_lazy directly m1 <- rbind( c(1, 0.81, 0), c(1, 0.4972376, 0.4972376) ) testphi <- slMatrix(init = m1) myf <- pcarma_acvf_lazy(testphi, testtheta, si2, 2, 0, 2, maxlag = 10) myf(1:2, 0:9) # get a matrix of values all(myf(1:2, 0:9) == pcAR2acf(m, si2, 2, maxlag = 9)) # TRUE
Fit a PC-ARMA model to a periodic autocovariance function.
pcarma_acvf2model(acf, model, maxlag)pcarma_acvf2model(acf, model, maxlag)
acf |
a periodic autocovariance function, an object of class
|
model |
a pc- arma model, an object of class
|
maxlag |
not used. (todo: check!) |
~Describe the value returned If it is a LIST, use
comp1 |
Description of 'comp1' |
comp2 |
Description of 'comp2' |
...
Georgi N. Boshnakov
Boshnakov GN (1996). “Recursive computation of the parameters of periodic autoregressive moving-average processes.” J. Time Ser. Anal., 17(4), 333–349. ISSN 0143-9782, doi:10.1111/j.1467-9892.1996.tb00281.x.
data(ex1f) pc3 <- slMatrix(period=2,maxlag=5,f=ex1f,type="tt") # pcarma_param_system(pc3, NULL, NULL, 2, 0, 2) parsys <- pcarma_param_system(pc3, NULL, NULL, c(2,2), 0, 2) param <- solve(parsys$A,parsys$b) # res <- pcarma_acvf2model(pc3, list(p=c(1,2),q=0,period=2)) # res <- pcarma_acvf2model(pc3, list(p=c(1,2),q=0)) # res <- pcarma_acvf2model(pc3, list(p=c(1,2),period=2)) res <- pcarma_acvf2model(pc3, list(p=c(1,2))) print(param) print(res)data(ex1f) pc3 <- slMatrix(period=2,maxlag=5,f=ex1f,type="tt") # pcarma_param_system(pc3, NULL, NULL, 2, 0, 2) parsys <- pcarma_param_system(pc3, NULL, NULL, c(2,2), 0, 2) param <- solve(parsys$A,parsys$b) # res <- pcarma_acvf2model(pc3, list(p=c(1,2),q=0,period=2)) # res <- pcarma_acvf2model(pc3, list(p=c(1,2),q=0)) # res <- pcarma_acvf2model(pc3, list(p=c(1,2),period=2)) res <- pcarma_acvf2model(pc3, list(p=c(1,2))) print(param) print(res)
Given a PCARMA model, create a function for computing autocovariances or coefficients of the corresponding infinite moving average representation or prepare the linear system whose solution provides the first few autocovariances of the model.
pcarma_acvf_lazy(phi, theta, sigma2, p, q, period, maxlag = 100) pcarma_h_lazy(phi, theta, p, q, period, maxlag = 200) pcarma_acvf_system(phi, theta, sigma2, p, q, period) pcarma_param_system(acf, h, sigma2, p, q, period) pcarma_h(h, na = NA)pcarma_acvf_lazy(phi, theta, sigma2, p, q, period, maxlag = 100) pcarma_h_lazy(phi, theta, p, q, period, maxlag = 200) pcarma_acvf_system(phi, theta, sigma2, p, q, period) pcarma_param_system(acf, h, sigma2, p, q, period) pcarma_h(h, na = NA)
phi |
the autoregression parameters, an object of class |
theta |
the moving average parameters, an object of class |
sigma2 |
the innovation variances, an object of class
|
p |
the (maximal) autoregression order or the autoregression orders. |
q |
the (maximal) moving average order or the moving average orders. |
period |
number of seasons in an epoch |
maxlag |
maximal lag for which the result is stored internally. |
acf |
the autocovariance function, an object of class pcAcvf, slMatrix, or similar |
h |
|
na |
not used currently, controls what to do for large lags. |
pcarma_acvf_lazy creates a function that will compute (on
demand) values of the acf by a recursive formula. Computed values
are stored internally for lags up to maxlag.
pcarma_acvf_system forms a linear system for the calculation
of autocovariances from the parameters of a pc-arma model. The
argument theta is not used if and phi is not
used if .
pcarma_param_system takes
the periodic autocovariances of a pc-arma model and computes a
matrix and a vector representing the linear system whose solution
provides the parameters of the model.
Scalar p specifies the same autoregression order for each
season, similarly for q. p and q may be
vectors of length period specifying the order for each season
individually. In the latter case the solution of the system may not
be a proper model or, if it is, its autocovariances may not be the
ones used here! See the references for details.
The class of acf is not required to be one of those
explicitly listed above, but it should understand their indexing
conventions, similarly for sigma2.
For pure autoregression, , the arguments h and
sigma2 are ignored. TODO: add sigma2 (if supplied) to
the returned list?
pcarma_h_lazy: h(t,i) are the coefficients in infinite the
moving average representation of the pc.arma model. The calculations
use formula (4.4) from my paper (or elsewhere) with internal storage
(in an slMatrix) of calculated results (for i<maxlag) and recursive
calls to itself. So, it is not necessary to compute h(t,i) in any
particular order.
pcarma_h Function to create a function for lazy computation
of h(t,i) in pc.arma models
Takes a matrix of h(t,i) coefficeints and returns a function that
calculates h(t,i) from my paper xxx. The returned value can be used
in the same way as that of pcarma_h_lazy.
a function taking two arguments t and k such that for
scalar t and k the call f(t,k) will return
EX(t)X(t-k). If either of the arguments is a vector, then
f(t,k) returns a matrix of size (length(t),length(k))
containing the respective autocovariances.
a function, say h. In calls to h, if both arguments
are scalars h(t,i) returns $h_t,i$. If at least one of the
arguments is a vector a matrix of values of $h$ is returned.
a list with two components representing the linear system:
The
matrix of the system, an object of class "matrix".
The right-hand side of the system, a vector of length
, an object of class "vector".
can be used to get a vector of the
autocovariances in the following order (d is the period, p is the
maximal AR order):
A list with components representing the linear system and the AR and MA orders:
The matrix of the system
The right-hand side of the system
The AR order
The MA order
will return a vector of the parameters of the
pc-arma model: all parameters for the first season, followed by all
parameters for the second seasons and so on. For each season the
parameters are in the following order (s is the current season, d is
the period, and are the corresponding AR and
MA orders):
a function, say h. In calls to h, if both arguments
are scalars h(t,i) returns $h_t,i$. If at least one of the
arguments is a vector a matrix of values of $h$ is returned.
Analogous to pcarma_h_lazy.
for pcarma_acvf_lazy: The recursion may become extremely slow for lags greater than
maxlag. If large lags are likely to be needed the argument
maxlag should be used to increase the internal storage. The
default for maxlag currently is 100.
Georgi N. Boshnakov
Boshnakov GN (1996). “Recursive computation of the parameters of periodic autoregressive moving-average processes.” J. Time Ser. Anal., 17(4), 333–349. ISSN 0143-9782, doi:10.1111/j.1467-9892.1996.tb00281.x.
## periodic acf of Lambert-Lacroix data(ex1f) (pc3 <- slMatrix(period = 2, maxlag = 5, f = ex1f, type = "tt")) ## find the parameters s3 <- pcarma_param_system(pc3, NULL, NULL, 2, 0, 2) coef3 <- solve(s3$A, s3$b) pcarma_unvec(list(p = 2, q = 0, period = 2, param = coef3)) ## actually, the model is PAR(1,2): s3a <- pcarma_param_system(pc3, NULL, NULL, c(1, 2), 0, 2) coef3a <- solve(s3a$A, s3a$b) pcarma_unvec(list(p = c(1,2), q = 0, period = 2, param = coef3a)) ## prepare test parameters for a PAR(2) model with period=2. ## (rounded to 6 digits from the above example. m1 <- rbind(c(1, 0.81, 0), c(1, 0.4972376, 0.4972376) ) m2 <- rbind(c(1, 0, 0), c(1, 0, 0) ) testphi <- slMatrix(init = m1) testtheta <- slMatrix(init = m2) si2 <- PeriodicVector(c(0.3439000, 0.1049724)) # # or si2 <- c(1,1) ## acf from parameters myf <- pcarma_acvf_lazy(testphi, testtheta, si2, 2, 0, 2, maxlag = 110) myf(1,4) # compute a value a1 <- myf(1:2,0:9) # get a matrix of values ## h from parameters h <- pcarma_h_lazy(testphi, testtheta, 2, 2, 2) h(3, 2) # a scalar h1 <- h(1:2, 1:4) # a matrix ## compute acvf from parameters ( acfsys <- pcarma_acvf_system(testphi, testtheta, si2, 2, 0, 2) ) acfvec <- solve(acfsys$A, acfsys$b) acf1 <- slMatrix(acfvec, period = 2) ## TODO: examples wirh q != 0## periodic acf of Lambert-Lacroix data(ex1f) (pc3 <- slMatrix(period = 2, maxlag = 5, f = ex1f, type = "tt")) ## find the parameters s3 <- pcarma_param_system(pc3, NULL, NULL, 2, 0, 2) coef3 <- solve(s3$A, s3$b) pcarma_unvec(list(p = 2, q = 0, period = 2, param = coef3)) ## actually, the model is PAR(1,2): s3a <- pcarma_param_system(pc3, NULL, NULL, c(1, 2), 0, 2) coef3a <- solve(s3a$A, s3a$b) pcarma_unvec(list(p = c(1,2), q = 0, period = 2, param = coef3a)) ## prepare test parameters for a PAR(2) model with period=2. ## (rounded to 6 digits from the above example. m1 <- rbind(c(1, 0.81, 0), c(1, 0.4972376, 0.4972376) ) m2 <- rbind(c(1, 0, 0), c(1, 0, 0) ) testphi <- slMatrix(init = m1) testtheta <- slMatrix(init = m2) si2 <- PeriodicVector(c(0.3439000, 0.1049724)) # # or si2 <- c(1,1) ## acf from parameters myf <- pcarma_acvf_lazy(testphi, testtheta, si2, 2, 0, 2, maxlag = 110) myf(1,4) # compute a value a1 <- myf(1:2,0:9) # get a matrix of values ## h from parameters h <- pcarma_h_lazy(testphi, testtheta, 2, 2, 2) h(3, 2) # a scalar h1 <- h(1:2, 1:4) # a matrix ## compute acvf from parameters ( acfsys <- pcarma_acvf_system(testphi, testtheta, si2, 2, 0, 2) ) acfvec <- solve(acfsys$A, acfsys$b) acf1 <- slMatrix(acfvec, period = 2) ## TODO: examples wirh q != 0
Handle a simple list specification of pcarma models. Functions to convert to and from a representation appropriate for handing on to optimisation functions.
pcarma_prepare(model, type) pcarma_unvec(model) pcarma_tovec(model)pcarma_prepare(model, type) pcarma_unvec(model) pcarma_tovec(model)
model |
specification of a pcarma model, a list, see Details. |
type |
not used. |
These functions work with a specification of a pcarma model as a list
with components period, p, q, param,
phi, theta and si2, see also section ‘Values’.
The functions do not necessarily need or examine all these components.
Argument model is a list with components as accepted by
pcarma_prepare. Details are below but the guiding rule is that
there are sensible defaults for absent components.
pcarma_prepare gives a standard representation of model, in
the sense that it ensures that the model has components period,
p and q, such that p and q are vectors of
length period. pcarma_prepare does not examine any other
components of the model. (TODO: do the same for the
innovation variance?)
If model$period is NULL, pcarma_prepare sets it to the
length of the longer of model$p and model$q. If
model$p is a scalar it is extended with rep(model$p,
period). Missing or NULL model$p is equivalent to
model$p = 0. model$q is processed analogously.
The net effect is that period, p and q will be set
as expected as long as period is given or at least one of the
other two is of length equal to the period. A warning is issued if
period <= 1 (it is all too easy to give scalar values for
p and q and forget to set the period, in which case
period will be deduced to be one).
A number of functions (including pcarma_tovec and
pcarma_unvec) dealing with the list representation of pcarma
models start by calling pcarma_prepare to avoid the need for
handling all possible cases.
pcarma_tovec returns a list with components p,
q and param, where param is a numeric vector
containing the pcarma parameters and the innovations variances and
thus is suitable for optimisation functions. Notice that it is
component param that is a vector. The reason that pcarma_tovec
returns a list, is that the caller may need to do further work before
calling a generic optimisation function. For exampe, it may wish to
dop the variances from the vector.
pcarma_unvec(model) performs the inverse operation. It takes a
list like that produced by pcarma_tovec and converts it to a
detailed list containing the components of the model.
for pcarma_unvec, a list with components:
p |
autoregressive orders, numeric vector |
q |
moving average orders, numeric vector |
si2 |
innovation variances |
phi |
autoregressive parameters |
theta |
moving average parameters |
for pcarma_tovec, a list with components:
p |
autoregressive order |
q |
moving average order |
param |
parameters of the model, a numeric vector. TODO: give the order of the parameters in the vector! |
for pcarma_prepare, a list as pcarma_unvec, see also
Details.
The specification and the functions were created ad hoc to get the computations going and are not always consistent with other parts of the package.
Georgi N. Boshnakov
pcCycle() is a generic function with methods for creating,
converting, modifying, and extracting cycle objects. BuiltinCycle()
is a function to create cycle objects from the builtin cycle classes.
pcCycle(x, type, ...) BuiltinCycle(n, coerce = FALSE, first = 1, stop = TRUE)pcCycle(x, type, ...) BuiltinCycle(n, coerce = FALSE, first = 1, stop = TRUE)
x |
an object, methods include numeric, character and cyclic objects, see Details. |
type |
class of the result. If equal to |
... |
further arguments for methods. |
n |
number of seasons, an integer. |
coerce |
if |
first |
which season is first for this object. |
stop |
if |
pcCycle serves as both a constructor and extractor of cycle
objects. It is meant to just do the right thing, relieving the user
from the burden of specifying a particular cycle class.
If x is numeric it constructs a cycle object with period
x and additional properties as specified by the other
arguments. If x is a character string, it is taken to be the
name of one of the builtin cycles.
pcCycle can be used to create a modified version of a cycle
object and/or convert it to another cycle type. This is done by
providing a cycle object as argument x, i.e. one inheriting
from "BasicCycle".
If x inherits from "Cyclic", pcCycle returns its
cycle component.
Argument type should be rarely needed, except maybe to
conveniently force conversion of the builtin type to an ordinary type.
The descriptions of the individual methods in section Methods give some further specific details.
BuiltinCycle is a convenience function to create objects from
builtin cycle classes by specifying the number of seasons. The
builtin cycle classes are esseintially fixed, except that which season
is considered first can be changed using argument first. If
other modifications are desired, convert the returned builtin cycle
object to class "SimpleCycle". This can be done also in the
call to BuiltinCycle() by specifying coerce = TRUE.
By default, BuiltinCycle throws an error if there is no builtin
class with the requested number of seasons. Set argument stop
to FALSE to create an object from class "BareCycle" instead
(and it will be converted to "SimpleCycle" if coerce =
TRUE). Argument stop is mainly for programming.
for pcCycle, an object from one of the cycle classes;
for BuiltinCycle, an object from one of the builtin classes,
coerced if requested.
signature(x = "numeric", type = "missing")creates a cycle object with period x. If x is the only
argument, a "BareCycle" object is created, otherwise the
constructor of "SimpleCycle" is invoked with all arguments
except type passed on to it.
signature(x = "character", type = "missing")creates an object from the class specified by x.
Currently this is equivalent to new(x, ...) but somewhat
more portable. Future amendments may use a more suitable class
for some combinations of the arguments. Also, if a class is renamed,
a code will be inserted here to create an equivalent object.
signature(x = "numeric", type = "character")signature(x = "character", type = "character")first call the method with type = "missing", then
convert the result to class type.
signature(x = "Cyclic", type = "ANY")extracts the cycle component of x (x@cycle).
Currently ignores the remaining arguments.
signature(x = "BasicCycle", type = "missing")convert an object from any cycle class to class
"SimpleCycle". This is like as(x, "SimpleCycle") but
can have further arguments.
signature(x = "BasicCycle", type = "character")convert an object from any cycle class to class
type.
signature(x = "ts", type = "missing")signature(x = "ts", type = "character")when x is of class "ts", extract the frequency and
convert it to a cycle class. Just as for "ts", certain
frequencies are taken to correspond to specific classes. While base
R treats periodicities 4 and 12 specially, pcCycle extends
this to all builtin classes in pcts. Argument type can be
used to overwrite this default behaviour by requesting a specific
class. In particular, type = "BareCycle" and type = ""
cause the result to be "BareCycle".
signature(x = "PeriodicTimeSeries", type = "missing")signature(x = "PeriodicTimeSeries", type = "character")extract the cycle part of an object inheriting from
"PeriodicTimeSeries", currently "PeriodicTS" or
"PeriodicMTS". Argument type can be used to force the
result to be from a specific cycle class, as in the methods for
"ts".
Georgi N. Boshnakov
allSeasons for further examples,
class BuiltinCycle for the available builtin
classes and more examples,
Pctime for representation of dates and conversion
from/to datetime objects
## pcCycle pcCycle(4) pcCycle(4, seasons = c("Spring", "Summer", "Autumn", "Winter")) pcCycle("QuarterYearCycle") BuiltinCycle(4) # same, recommended pcCycle("QuarterYearCycle", type = "BareCycle") pcCycle("QuarterYearCycle", type = "SimpleCycle") ## BuiltinCycle BuiltinCycle(2) # "OpenCloseCycle" BuiltinCycle(4) # "QuarterYearCycle" BuiltinCycle(5) # five day week cycle BuiltinCycle(7) # "DayWeekCycle" BuiltinCycle(12) # "MonthYearCycle" BuiltinCycle(48) # "Every30MinutesCycle" ## error, since there is no builtin cycle with 19 seasons: ## BuiltinCycle(19) ## use stop = FALSE to reate a default cycle in this case BuiltinCycle(19, stop = FALSE) BuiltinCycle(19, coerce = TRUE, stop = FALSE)## pcCycle pcCycle(4) pcCycle(4, seasons = c("Spring", "Summer", "Autumn", "Winter")) pcCycle("QuarterYearCycle") BuiltinCycle(4) # same, recommended pcCycle("QuarterYearCycle", type = "BareCycle") pcCycle("QuarterYearCycle", type = "SimpleCycle") ## BuiltinCycle BuiltinCycle(2) # "OpenCloseCycle" BuiltinCycle(4) # "QuarterYearCycle" BuiltinCycle(5) # five day week cycle BuiltinCycle(7) # "DayWeekCycle" BuiltinCycle(12) # "MonthYearCycle" BuiltinCycle(48) # "Every30MinutesCycle" ## error, since there is no builtin cycle with 19 seasons: ## BuiltinCycle(19) ## use stop = FALSE to reate a default cycle in this case BuiltinCycle(19, stop = FALSE) BuiltinCycle(19, coerce = TRUE, stop = FALSE)
Fit PAR models using least squares. The model may contain intercepts and linear trends, seasonal or non-seasonal.
pclsdf(x, d, lags = integer(0), sintercept = TRUE, sslope = FALSE, intercept = FALSE, slope = FALSE, xreg, contrasts = NULL, seasonof1st = NULL, coefonly = FALSE)pclsdf(x, d, lags = integer(0), sintercept = TRUE, sslope = FALSE, intercept = FALSE, slope = FALSE, xreg, contrasts = NULL, seasonof1st = NULL, coefonly = FALSE)
x |
time series, a numeric vector. |
d |
period, an integer. |
lags |
an integer vector, typically |
sintercept |
if TRUE include seasonal intercepts. |
sslope |
if TRUE include seasonal linear trend. |
intercept |
if TRUE include non-seasonal intercept. |
slope |
if TRUE include non-seasonal linear trend. |
xreg |
additional regressors, not used currently. |
contrasts |
contrasts to use for the seasons factor variable. |
seasonof1st |
season of the first observation in the time series, see Details. |
coefonly |
if TRUE, return only the parameters of the fitted
model, otherwise include also the object returned by |
This function fits PAR models by the method of least squares. Seasonal intercepts are included by default. Non-seasonal intercepts are available, as well as seasonal and non-seasonal linear trend. Separate arguments are provided, so that any combination of seasonal and non-seasonal intercepts and slopes can be specified.
If coefonly is TRUE, pclsdf returns only the estimated
parameters, otherwise it includes additional statistical information,
see section Note for the current details.
A list with the components listed below. Some components are present only if included in the model specification.
par |
the PAR coefficients, a matrix with a row for each season. |
sintercept |
(if specified) seasonal intercepts, a numeric vector. |
sigma2hat |
innovation variances. |
formula.char |
the formula used in the call of |
fit |
(if |
Currently, pclsdf prepares a model formula according to the
specification and calls lm to do the fitting. Component "fit"
in the result (available when coefonly = FALSE) contains the
raw fitted object returned by lm. Statistical inference based
on this object would, in general, not be justified for correlated
data.
todo: currently some of the parameters are returned only via the
fitted object from lm.
Georgi N. Boshnakov
## data(dataFranses1996) cu <- pcts(dataFranses1996[ , "CanadaUnemployment"]) cu <- window(cu, start = availStart(cu), end = availEnd(cu)) pclsdf(cu, 4, 1:2, sintercept = TRUE) pclsdf(austres, 4, lags = 1:3) pclsdf(austres, 4, lags = 1:3, sintercept = TRUE) pclsdf(austres, 4, lags = 1:3, sintercept = TRUE, sslope = TRUE) x <- rep(1:4,10) pclsdf(x, 4, lags = 1:3, sintercept = TRUE, sslope = TRUE) ## this is for the version when contrasts arg. was passed on directly to lm. ## tmp1 <- pclsdf(austres, 4, lags = 1, sintercept = FALSE, sslope = TRUE, ## contrasts = list(Season = "contr.sum" ))## data(dataFranses1996) cu <- pcts(dataFranses1996[ , "CanadaUnemployment"]) cu <- window(cu, start = availStart(cu), end = availEnd(cu)) pclsdf(cu, 4, 1:2, sintercept = TRUE) pclsdf(austres, 4, lags = 1:3) pclsdf(austres, 4, lags = 1:3, sintercept = TRUE) pclsdf(austres, 4, lags = 1:3, sintercept = TRUE, sslope = TRUE) x <- rep(1:4,10) pclsdf(x, 4, lags = 1:3, sintercept = TRUE, sslope = TRUE) ## this is for the version when contrasts arg. was passed on directly to lm. ## tmp1 <- pclsdf(austres, 4, lags = 1, sintercept = FALSE, sslope = TRUE, ## contrasts = list(Season = "contr.sum" ))
Fit a periodically integrated autoregressive model.
pclspiar(x, d, p, icoef = NULL, parcoef = NULL, sintercept = FALSE, seasonof1st = 1, weights = TRUE, itol = 1e-07, maxniter = 1000)pclspiar(x, d, p, icoef = NULL, parcoef = NULL, sintercept = FALSE, seasonof1st = 1, weights = TRUE, itol = 1e-07, maxniter = 1000)
x |
time series. |
d |
period. |
p |
order of the model, a positive integer, see Details. |
icoef |
initial values for the periodic integration coefficients. If missing
or |
parcoef |
not used currently. |
sintercept |
if |
seasonof1st |
season of the first observation. |
weights |
if |
itol |
threshold value for the stopping criterion. |
maxniter |
maximum number of iterations. |
This function fits a periodically integrated autoregressive model
using non-linear least squares. The order of integration is one and
the order of the periodically correlated part is p - 1. So,
p must be greater than or equal to one.
If weights = TRUE the non-linear optimisation is done with
weights inversely proportional to the innovation variances for the
seasons, otherwise the unweighted sum of squared residuals is
minimised.
a list currently containing the following elements:
icoef |
coefficients of the periodic integration filter. |
parcoef |
coefficients of the PAR filter. |
sintercept |
seasonal intercepts. |
sigma2hat |
innovation variances. |
Georgi N. Boshnakov
Franses PH (1996). Periodicity and Stochastic Trends In Economic Time Series. Oxford University Press Inc., New York.
Franses PH, Paap R (2004). Periodic Time Series Models. Oxford University Press Inc., New York.
Boshnakov GN, Iqelan BM (2009). “Generation of time series models with given spectral properties.” J. Time Series Anal., 30(3), 349–368. ISSN 0143-9782, doi:10.1111/j.1467-9892.2009.00617.x.
## see also the examples for fitPM() ts1 <- window(dataFranses1996[ , "CanadaUnemployment"], start = c(1960, 1), end = c(1987, 4)) pclspiar(ts1, 4, p = 1, sintercept = TRUE) pclspiar(ts1, 4, p = 2, sintercept = TRUE)## see also the examples for fitPM() ts1 <- window(dataFranses1996[ , "CanadaUnemployment"], start = c(1960, 1), end = c(1987, 4)) pclspiar(ts1, 4, p = 1, sintercept = TRUE) pclspiar(ts1, 4, p = 2, sintercept = TRUE)
Compute periodic mean, generic function.
pcMean(object, ...) ## S4 method for signature 'numeric' pcMean(object, nseasons, ...) ## S4 method for signature 'matrix' pcMean(object, nseasons, ...) ## S4 method for signature 'PeriodicTS' pcMean(object, ...) ## S4 method for signature 'PeriodicMTS' pcMean(object, ...)pcMean(object, ...) ## S4 method for signature 'numeric' pcMean(object, nseasons, ...) ## S4 method for signature 'matrix' pcMean(object, nseasons, ...) ## S4 method for signature 'PeriodicTS' pcMean(object, ...) ## S4 method for signature 'PeriodicMTS' pcMean(object, ...)
object |
an object for which periodic mean makes sense. |
nseasons |
number of seasons. |
... |
further arguments for methods. |
For univariate periodic time series, pcMean computes the mean
for each season and returns a named vector. For multivariate periodic
time series, the result is a matrix with one column for each variable.
The methods for "numeric" and "matrix" are equivalent to
those for "PeriodicTS" and "PeriodicMTS",
respectively. The difference is that the latter two don't need
argument nseasons and take the names of the seasons from
object.
Argument na.rm = TRUE can be used to omit NA's.
In the univariate case, when length(object) is an integer
multiple of the number of seasons the periodic mean is equivalent to
computing the row means of matrix(object, nrow = nseasons).
numeric or matrix for the methods described here, see section ‘Details’.
signature(object = "matrix")signature(object = "numeric")signature(object = "PeriodicMTS")signature(object = "PeriodicTS")signature(object = "VirtualPeriodicArmaModel")Georgi N. Boshnakov
pcApply which applies an arbitrary function by season
pcMean(pcts(presidents)) pcMean(pcts(presidents), na.rm = TRUE) pcMean(pcts(dataFranses1996)[2:5], na.rm = TRUE) pcMean(1:20, nseasons = 4) m <- matrix(1:20, nrow = 4) all(apply(m, 1, mean) == pcMean(1:20, nseasons = 4)) # TRUEpcMean(pcts(presidents)) pcMean(pcts(presidents), na.rm = TRUE) pcMean(pcts(dataFranses1996)[2:5], na.rm = TRUE) pcMean(1:20, nseasons = 4) m <- matrix(1:20, nrow = 4) all(apply(m, 1, mean) == pcMean(1:20, nseasons = 4)) # TRUE
Plot periodic time series.
## S3 method for class 'PeriodicTimeSeries' boxplot(x, ...) ## S3 method for class 'PeriodicTimeSeries' monthplot(x, ylab = deparse(substitute(x)), base, ...)## S3 method for class 'PeriodicTimeSeries' boxplot(x, ...) ## S3 method for class 'PeriodicTimeSeries' monthplot(x, ylab = deparse(substitute(x)), base, ...)
x |
a periodic time series object. |
... |
further arguments to be passed to the plotting function. |
ylab |
label for the y-axis, only used for univariate time series. |
base |
a function for use for computing reference lines. |
Functions for periodic/seasonal plots and boxplots.
Georgi N. Boshnakov
ap <- pcts(AirPassengers) monthplot(ap) boxplot(ap) fr23 <- pcts(dataFranses1996[ , 2:3]) monthplot(fr23) boxplot(fr23)ap <- pcts(AirPassengers) monthplot(ap) boxplot(ap) fr23 <- pcts(dataFranses1996[ , 2:3]) monthplot(fr23) boxplot(fr23)
Test for periodicity
pcTest(x, nullmodel, nseasons, ...)pcTest(x, nullmodel, nseasons, ...)
x |
the object to be tested, e.g. a time series or a periodic acf |
nullmodel |
specification of the test to be performed |
nseasons |
number of seasons |
... |
additional arguments to be passed on to methods |
This is a generic function which acts as a dispatcher for various tests for periodicity and periodic correlation.
x is typically a time series but conceptually it is an object
containing the statistics needed for carrying out the requested test.
For example, x may be the periodic autocovariance function for
tests based on sample autocorrelations and autocovariances.
The method with signature (x = "ANY", nullmodel = "character") may
be considered as default for pcTest. The “real” default
method simply prints an error message.
a list containing the results of the requested test, see the individual methods for details
signature(x = "ANY", nullmodel = "character")Argument nullmodel specifies the test to be performed.
It should be a single character string. If it is one of
the strings recognised by this method, the test specified below is
carried out. Otherwise nullmodel is taken to be the name of a
function which is called with arguments (x,...).
Currently, the following character strings are recognised:
Box test for (non-periodic) white noise, simply calls Box.test.
Franses (1996) test for periodic integration.
signature(x = "slMatrix", nullmodel = "character")x here is the periodic autocovariance function. This method
works similarly to the method for signature (x = "ANY",
nullmodel = "character"), see its description.
Currently, the following character strings are recognised:
Ljung-Box test for periodic white noise,
McLeod test for periodic correlation.
signature(x = "numeric", nullmodel = "character")signature(x = "PeriodicTimeSeries", nullmodel = "character")TODO: critical values
Georgi N. Boshnakov
test_piar,
pwn_McLeodLjungBox_test
periodic_acf1_test
cu <- pcts(dataFranses1996[ , "CanadaUnemployment"]) cu <- window(cu, start = availStart(cu), end = availEnd(cu)) test_piar(cu, 4, 1, sintercept = TRUE) pcTest(cu, "piar", 4, 1, sintercept = TRUE) if(require(partsm)){ # same with LRurpar.test from partsm LRurpar.test(cu, list(regular = c(0,0,0), seasonal = c(1,0), regvar = 0), p = 1) }cu <- pcts(dataFranses1996[ , "CanadaUnemployment"]) cu <- window(cu, start = availStart(cu), end = availEnd(cu)) test_piar(cu, 4, 1, sintercept = TRUE) pcTest(cu, "piar", 4, 1, sintercept = TRUE) if(require(partsm)){ # same with LRurpar.test from partsm LRurpar.test(cu, list(regular = c(0,0,0), seasonal = c(1,0), regvar = 0), p = 1) }
Class "Pctime" is an S3 class inheriting from the base R
datetime class "POSIXct". It has methods for conversion between
datetimes and the pcts cycle-season pairs, as well as convenience
methods for a few other functions.
Pctime(x, cycle, ...) as_Pctime(x, ...) ## S3 method for class 'Pctime' x[i, j, drop = TRUE] ## S3 method for class 'Pctime' x[[..., drop = TRUE]] ## S3 method for class 'Cyclic' as_Pctime(x, ...) ## S3 method for class 'PeriodicTimeSeries' as_Pctime(x, ...)Pctime(x, cycle, ...) as_Pctime(x, ...) ## S3 method for class 'Pctime' x[i, j, drop = TRUE] ## S3 method for class 'Pctime' x[[..., drop = TRUE]] ## S3 method for class 'Cyclic' as_Pctime(x, ...) ## S3 method for class 'PeriodicTimeSeries' as_Pctime(x, ...)
x |
for |
cycle |
a positive integer, cycle object, or missing. |
i |
subscript |
j |
noi used |
drop |
not used |
... |
further argument for methods. |
Pctime represents periodic times with cycle specification
contained in attribute "cycle". It is basically datetime
(inheriting from "POSIXct") with additional attribute(s).
For printing Pctime objects are shown as cycle-season pairs. To print
in other formats, just convert them using as_datetime or other
suitable function. Note though that some cycles in pcts do not have
natural datetime representation. For them, Pctime sets it arbitrarilly
as the number of seconds from a origin.
The seasons in cycle-season pairs are numbered from one to the number of seasons. Names and abbreviations are used when available and this is the case for all builtin cycles and partial cycles obtained from them.
The cycles in cycle-season pairs are numbered from a starting point.
For years, it is what is expected. For cycles representing weeks, week 1
is the first ISO week of 1970, so c(1,1) corresponds to
1969-12-29. For some other cycle classes c(1,1) also corresponds
to the first time in the first ISO week of 1970.
Subsetting with "[" keeps the Pctime class, while
"[[" returns a datetime object. Other standard functions work
with Pctime objects, as well, including seq.
A common source of frustration is the accidental use of as.Date
or as_date, instead of as.POSIXlt or as_datetime.
These four are often equivalent, most notably for monthly, quarterly and
daily observations but, in general, conversion to dates drops the
fractional day part of a datetime.
The default time zone is UTC. Other time zones can be used since the calculations use standard datetime and date functions from base R and package lubridate (Grolemund and Wickham 2011), but currently this has not been tested.
for Pctime, an object from S3 class Pctime
Grolemund G, Wickham H (2011). “Dates and Times Made Easy with lubridate.” Journal of Statistical Software, 40(3), 1–25. doi:10.18637/jss.v040.i03.
## a bare bone date for four seasons pct4 <- Pctime(c(2020, 2), pcCycle(4)) pct4 ## quarterly cycle Pctime("2020-04-01", BuiltinCycle(4)) pctQ <- Pctime(c(2020, 2), BuiltinCycle(4)) # same pctQ ## day-in-week cycle ## c(1, 1) is the start of the first ISO week of 1970 weekW1S1 <- Pctime(c(1, 1), BuiltinCycle(7)) # W1 Mon weekW1S1 as_datetime(weekW1S1) Pctime("1970-01-01", BuiltinCycle(7)) # W1 Thu pctW1Th <- Pctime(c(1, 4), BuiltinCycle(7)) # same pctW1Th Pctime("2020-04-01", BuiltinCycle(7)) pctW2623Wed <- Pctime(c(2623, 3), BuiltinCycle(7)) # same pctW2623Wed as_datetime(pctW2623Wed) ## Monday-Friday week - a partial cycle derived from DayOfWeekCycle BuiltinCycle(5) pctMF <- Pctime("2020-04-03", BuiltinCycle(5)) # Fri seq(pctMF, length.out = 10) # note: Sat, Sun are skipped Pctime("2020-04-04", BuiltinCycle(5)) # Sat, not in the cycle ## monthly cycle Pctime("2020-04-01", BuiltinCycle(12)) pctY2020Apr <- Pctime(c(50, 4), BuiltinCycle(12)) # same pctY2020Apr as_datetime(pctW2623Wed) ## Pctime can hold a vector of times ap <- pcts(AirPassengers) aptime <- Pctime(ap) # as_Pctime(ap) aptime[1:12] # keep Pctime class aptime[1] aptime[[1]] # drop Pctime class head(aptime) tail(aptime) apdates <- as_datetime(ap) head(apdates) tail(apdates)## a bare bone date for four seasons pct4 <- Pctime(c(2020, 2), pcCycle(4)) pct4 ## quarterly cycle Pctime("2020-04-01", BuiltinCycle(4)) pctQ <- Pctime(c(2020, 2), BuiltinCycle(4)) # same pctQ ## day-in-week cycle ## c(1, 1) is the start of the first ISO week of 1970 weekW1S1 <- Pctime(c(1, 1), BuiltinCycle(7)) # W1 Mon weekW1S1 as_datetime(weekW1S1) Pctime("1970-01-01", BuiltinCycle(7)) # W1 Thu pctW1Th <- Pctime(c(1, 4), BuiltinCycle(7)) # same pctW1Th Pctime("2020-04-01", BuiltinCycle(7)) pctW2623Wed <- Pctime(c(2623, 3), BuiltinCycle(7)) # same pctW2623Wed as_datetime(pctW2623Wed) ## Monday-Friday week - a partial cycle derived from DayOfWeekCycle BuiltinCycle(5) pctMF <- Pctime("2020-04-03", BuiltinCycle(5)) # Fri seq(pctMF, length.out = 10) # note: Sat, Sun are skipped Pctime("2020-04-04", BuiltinCycle(5)) # Sat, not in the cycle ## monthly cycle Pctime("2020-04-01", BuiltinCycle(12)) pctY2020Apr <- Pctime(c(50, 4), BuiltinCycle(12)) # same pctY2020Apr as_datetime(pctW2623Wed) ## Pctime can hold a vector of times ap <- pcts(AirPassengers) aptime <- Pctime(ap) # as_Pctime(ap) aptime[1:12] # keep Pctime class aptime[1] aptime[[1]] # drop Pctime class head(aptime) tail(aptime) apdates <- as_datetime(ap) head(apdates) tail(apdates)
Create objects from periodic time series classes.
pcts(x, nseasons, start, ..., keep = FALSE)pcts(x, nseasons, start, ..., keep = FALSE)
x |
a time series. |
nseasons |
number of seasons. This argument is ignored by some methods. |
start |
the starting time of the time series, can be a |
keep |
if |
... |
further arguments to be passed on to methods. |
pcts creates periodic time series objects inheriting from
"PeriodicTimeSeries". The particular class depends on arguments
x and, in some cases, keep. The idea is that in normal
use the user does not care about the particular class. See section
‘Methods’ for further details.
Familiar functions from base-R work with the objects created by
pcts. The help page window describes such methods
and gives examples.
There are also methods for as for conversion to and from the
time series classes defined in package pcts.
an object inheriting from "PeriodicTimeSeries", the defaults
are "PeriodicTS" for univariate and "PeriodicMTS" and
for multivariate time series.
signature(x = "numeric", nseasons = "missing")signature(x = "numeric", nseasons = "numeric")signature(x = "numeric", nseasons = "BasicCycle")Creates an object of class "PeriodicTS", the native class for
univariate periodic time series in package "pcts".
signature(x = "matrix", nseasons = "missing")signature(x = "matrix", nseasons = "numeric")signature(x = "matrix", nseasons = "BasicCycle")Creates an object of class "PeriodicMTS", the native class
for multivariate periodic time series in package "pcts".
signature(x = "data.frame", nseasons = "ANY")Currently this just converts x to matrix and calls
pcts recursively. See the methods with x = "matrix" in
the signature.
signature(x = "ts", nseasons = "missing")signature(x = "ts", nseasons = "numeric")If keep = TRUE creates an object of class
"PeriodicTS_ts", otherwise the result is from
"PeriodicTS". The number of seasons is taken from the
"mts" object.
signature(x = "mts", nseasons = "missing")signature(x = "mts", nseasons = "numeric")If keep = TRUE creates an object of class
"PeriodicMTS_ts", otherwise the result is from
"PeriodicMTS". The number of seasons is taken from the
"ts" object.
signature(x = "xtsORzoo", nseasons = "missing")x needs to be a regular time series, possibly with missing
values for some times (technically, zoo::is.regular(x) should
give TRUE). For daily time series, the cycle is taken to be day of
week or a subcycle of it, most commonly Monday-Friday.
The implementation of this method is incomplete but for daily data
should work as described.
Georgi N. Boshnakov
PeriodicTS,
PeriodicMTS, the two main periodic time series
classes in the package;
dataFranses1996, Fraser2017,
four_stocks_since2016_01_01 for further examples;
window for extraction of subsets;
pcApply for applying a function to each season;
Vec,
tsVec,
pcMatrix for extraction of the core data
## convert a ts object, no need for further info pcts(AirPassengers, 12) ## numeric v24 <- rnorm(24) pcts(v24, nseasons = 4) # generic seasons pcts(v24, nseasons = BuiltinCycle(4)) # Quarter/Year ts1 <- pcts(v24, nseasons = BuiltinCycle(4), c(2006, 1)) # Quarter/Year with dates ## select subset of the seasons window(ts1, seasons = 3:4) ## matrix, multivariate pcts m24 <- matrix(v24, ncol =3) colnames(m24) <- c("A", "B", "C") pcts(m24, nseasons = 4) # generic seasons pcts(m24, nseasons = BuiltinCycle(4)) # Quarter/Year mts1 <- pcts(m24, nseasons = BuiltinCycle(4), c(2006, 1)) # Quarter/Year with dates mts1 ## select subset of the seasons for mutivariate window(mts1, seasons = 3:4)## convert a ts object, no need for further info pcts(AirPassengers, 12) ## numeric v24 <- rnorm(24) pcts(v24, nseasons = 4) # generic seasons pcts(v24, nseasons = BuiltinCycle(4)) # Quarter/Year ts1 <- pcts(v24, nseasons = BuiltinCycle(4), c(2006, 1)) # Quarter/Year with dates ## select subset of the seasons window(ts1, seasons = 3:4) ## matrix, multivariate pcts m24 <- matrix(v24, ncol =3) colnames(m24) <- c("A", "B", "C") pcts(m24, nseasons = 4) # generic seasons pcts(m24, nseasons = BuiltinCycle(4)) # Quarter/Year mts1 <- pcts(m24, nseasons = BuiltinCycle(4), c(2006, 1)) # Quarter/Year with dates mts1 ## select subset of the seasons for mutivariate window(mts1, seasons = 3:4)
Periodic time series objects for examples and tests. These objects are
from classes defined in package “pcts” and as a consequence are
not suitable for access with data().
pcts_exdata(x, envir = parent.frame())pcts_exdata(x, envir = parent.frame())
x |
a character vector giving the names of objects. If missing, all
available objects will be created. Can also be |
envir |
environment where the objects are put, the default is the environment of the caller. |
The requested objects are created and put in envir. Its
default is the environment of the caller, which should be sufficient
in most use cases.
The following objects are currently available:
ap, ap7to9, pcfr, pcfr2to4.
if x is NA, the names of the available objects.
Otherwise the function is called for the side effect of creating
objects in envir and the return value (the names of the created
objects) is usually discarded.
## the objects are created with something like: ap <- pcts(AirPassengers) ap7to9 <- window(ap, seasons = 7:9) pcfr <- pcts(dataFranses1996) pcfr2to4 <- pcfr[2:4]## the objects are created with something like: ap <- pcts(AirPassengers) ap7to9 <- window(ap, seasons = 7:9) pcfr <- pcts(dataFranses1996) pcfr2to4 <- pcfr[2:4]
These functions and classes are marked for removal and are provided temporarily for compatibility with older versions of package pcts only. Use the recommended renamed or new functions instead.
Class "FiveDayWeekCycle" is deprecated, use
BuiltinCycle(5) to create objects with equivalent
functionality, see BuiltinCycle.
has been renamed to sim_parCoef
has been renamed to sim_parAcvf
Functions for some basic operations with seasons.
pdSafeParOrder(p)pdSafeParOrder(p)
p |
autoregression order, a vector of integers. |
pdSafeParOrder(p) modifies the periodic AR order specified by vector
p. The modified order is such that the correspondence between
autocovariances and partial autocorrelations is one-to-one, see
the references for details.
a vector of integers
Georgi N. Boshnakov
Lambert-Lacroix S (2000). “On periodic autoregressive process estimation .” IEEE Transactions on Signal Processing, 48( 6 ), pp. 1800-1803.
Lambert-Lacroix S (2005). “ Extension of autocovariance coefficients sequence for periodically correlated processes.” Journal of Time Series Analysis, 26(6), pp. 423-435.
pdSafeParOrder(c(0,2)) pdSafeParOrder(c(2,3))pdSafeParOrder(c(0,2)) pdSafeParOrder(c(2,3))
Performs McLeod's test for periodic autocorrelation.
periodic_acf1_test(acf, nepochs)periodic_acf1_test(acf, nepochs)
acf |
sample periodic autocorrelation function |
nepochs |
the number of epochs used to get the acf |
The test statistic is a scaled sum of squares of lag 1 sample periodic autocorrelation coefficients, see McLeod (1993), eq. (5). The distribution is approximately chi-square under the null hypothesis of no periodic autocorrelation.
A list containing the following components:
statistic |
the value of the test statistic. |
pvalue |
the p-value associated with the test statistic. |
Georgi N. Boshnakov
McLeod AI (1993). “Parsimony, model adequacy and periodic correlation in time series forecasting.” Internat. Statist. Rev., 61(3), 387-393.
McLeod AI (1994). “Diagnostic checking of periodic autoregression models with application.” Journal of Time Series Analysis, 15(2), 221–233.
McLeod AI (1995). “Diagnostic checking of periodic autoregression models with application.” Journal of Time Series Analysis, 16(6), 647-648. doi:10.1111/j.1467-9892.1995.tb00260.x, This corrects some typos in the eponimous article McLeod (1994).
"PeriodicArmaFilter"
Class PeriodicArmaFilter.
Objects can be created by calls of the form new("PeriodicArmaFilter", ..., ar, ma, nseasons).
ar:Object of class "PeriodicBJFilter" ~~
ma:Object of class "PeriodicSPFilter" ~~
Class "VirtualArmaFilter", directly.
Class "VirtualMonicFilter", by class "VirtualArmaFilter", distance 2.
signature(from = "PeriodicArmaFilter", to = "PeriodicArFilter"): ...
signature(from = "PeriodicArmaFilter", to = "PeriodicMaFilter"): ...
signature(.Object = "PeriodicArmaFilter"): ...
signature(object = "PeriodicArmaFilter"): ...
signature(object = "PeriodicArmaFilter"): ...
Class PeriodicArmaModel.
Objects can be created by calls of the form new("PeriodicArmaModel", ar, ma, sigma2, ...).
sigma2:Object of class "numeric" ~~
ar:Object of class "PeriodicArFilter" ~~
ma:Object of class "PeriodicMaFilter" ~~
center:Object of class "numeric" ~~
intercept:Object of class "numeric" ~~
modelCycle:Object of class "BasicCycle" ~~
Class "VirtualPeriodicArmaModel", directly.
Class "PeriodicArmaSpec", directly.
Class "VirtualPeriodicFilterModel", by class "VirtualPeriodicArmaModel", distance 2.
Class "VirtualPeriodicStationaryModel", by class "VirtualPeriodicArmaModel", distance 2.
Class "PeriodicArmaFilter", by class "PeriodicArmaSpec", distance 2.
Class "VirtualPeriodicAutocovarianceModel", by class "VirtualPeriodicArmaModel", distance 3.
Class "VirtualPeriodicMeanModel", by class "VirtualPeriodicArmaModel", distance 3.
signature(x = "PeriodicArmaModel", maxlag = "ANY"): ...
signature(from = "PeriodicArmaModel", to = "list"): ...
signature(from = "PeriodicArmaModel", to = "PeriodicArModel"): ...
signature(object = "PeriodicArmaModel"): ...
Class PeriodicArmaSpec.
Objects can be created by calls of the form new("PeriodicArmaSpec", pcmean, pcintercept, ...).
sigma2:Object of class "numeric" ~~
ar:Object of class "PeriodicArFilter" ~~
ma:Object of class "PeriodicMaFilter" ~~
center:Object of class "numeric" ~~
intercept:Object of class "numeric" ~~
modelCycle:Object of class "BasicCycle" ~~
Class "PeriodicArmaFilter", directly.
Functions with methods for this class:
signature(.Object = "PeriodicArmaSpec"): ...
signature(object = "PeriodicArmaSpec"): ...
Class PeriodicArModel.
Objects can be created by calls of the form new("PeriodicArModel", ar, ma, sigma2, ...).
sigma2:Object of class "numeric" ~~
ar:Object of class "PeriodicArFilter" ~~
ma:Object of class "PeriodicMaFilter" ~~
center:Object of class "numeric" ~~
intercept:Object of class "numeric" ~~
modelCycle:Object of class "BasicCycle" ~~
Class "PeriodicArmaModel", directly.
Class "VirtualPeriodicArmaModel", by class "PeriodicArmaModel", distance 2.
Class "PeriodicArmaSpec", by class "PeriodicArmaModel", distance 2.
Class "VirtualPeriodicFilterModel", by class "PeriodicArmaModel", distance 3.
Class "VirtualPeriodicStationaryModel", by class "PeriodicArmaModel", distance 3.
Class "PeriodicArmaFilter", by class "PeriodicArmaModel", distance 3.
Class "VirtualPeriodicAutocovarianceModel", by class "PeriodicArmaModel", distance 4.
Class "VirtualPeriodicMeanModel", by class "PeriodicArmaModel", distance 4.
signature(x = "PeriodicArModel", maxlag = "ANY"): ...
signature(from = "PeriodicArmaModel", to = "PeriodicArModel"): ...
signature(model = "PeriodicArModel", x = "ANY"): ...
signature(model = "PeriodicArModel", x = "PeriodicMTS"): ...
signature(model = "PeriodicArModel", x = "PeriodicTS"): ...
signature(x = "PeriodicArModel"): ...
signature(object = "PeriodicArModel"): ...
Create objects from class PeriodicArModel
PeriodicArModel(object, ...)PeriodicArModel(object, ...)
object |
an object, can have one of a number of classes. |
... |
further arguments for methods. |
PeriodicArModel creates objects from class
PeriodicArModel. This is a generic function with dispatch methods on
the first argument.
an object from class "PeriodicArModel"
signature(object = "matrix")"object" gives the coefficients, one row per season.
signature(object = "numeric")"object" gives the model order. Its length is taken to be
the number of seasons. The coefficients are set to NA.
signature(object = "PeriodicMonicFilterSpec")signature(object = "VirtualPeriodicArmaModel")signature(object = "PeriodicMonicFilterSpec")signature(object = "VirtualPeriodicArmaModel")Class PeriodicAutocorrelations.
Objects can be created by calls of the form new("PeriodicAutocorrelations", ..., data).
modelCycle:Object of class "BasicCycle" ~~
data:Object of class "Lagged" ~~
Class "ModelCycleSpec", directly.
Class "FlexibleLagged", directly.
Class "VirtualPeriodicAutocorrelations", directly.
Class "Lagged", by class "FlexibleLagged", distance 2.
Class "VirtualPeriodicModel", by class "VirtualPeriodicAutocorrelations", distance 2.
signature(x = "PeriodicAutocorrelations", y = "missing"): ...
Class PeriodicAutocovariances.
Objects can be created by calls of the form new("PeriodicAutocovariances", ..., data).
modelCycle:Object of class "BasicCycle" ~~
data:Object of class "Lagged" ~~
Class "ModelCycleSpec", directly.
Class "FlexibleLagged", directly.
Class "VirtualPeriodicAutocovariances", directly.
Class "Lagged", by class "FlexibleLagged", distance 2.
Class "VirtualPeriodicModel", by class "VirtualPeriodicAutocovariances", distance 2.
signature(x = "PeriodicAutocovariances", maxlag = "ANY", lag_0 = "missing"): ...
signature(x = "PeriodicAutocovariances", maxlag = "ANY", lag_0 = "missing"): ...
A class for filters following the Box-Jenkins sign convention
Objects can be created by calls of the form new("PeriodicBJFilter", coef, order, ...).
coef:Object of class "matrix" ~~
order:Object of class "numeric" ~~
Class "PeriodicMonicFilterSpec", directly.
Class "VirtualBJFilter", directly.
Class "VirtualMonicFilterSpec", by class "PeriodicMonicFilterSpec", distance 2.
Class "VirtualMonicFilter", by class "VirtualBJFilter", distance 2.
signature(object = "PeriodicBJFilter", convention = "character"): ...
signature(from = "matrix", to = "PeriodicBJFilter"): ...
signature(from = "PeriodicBJFilter", to = "PeriodicSPFilter"): ...
signature(from = "PeriodicSPFilter", to = "PeriodicBJFilter"): ...
signature(object = "PeriodicBJFilter"): ...
signature(object = "PeriodicBJFilter"): ...
signature(object = "PeriodicBJFilter"): ...
Georgi N. Boshnakov
filterCoef for more details on the generics
## a toy filter of order c(3, 3, 3, 3) and 4 seasons co <- matrix(c(1, 1, 0, 2, 2, 2, 3, 0, 0, 4, 4, 4), nrow = 4, ncol = 3) ## these are equivalent: bj1 <- new("PeriodicBJFilter", coef = co) bj1b <- new("PeriodicBJFilter", coef = co, order = 3) bj1c <- new("PeriodicBJFilter", coef = co, order = c(3, 3, 3, 3)) identical(bj1b, bj1c) # TRUE identical(bj1, bj1b) # FALSE but only because classbj1@order is "integer" ## a more refined spec. for the order: show( new("PeriodicBJFilter", coef = co, order = c(2, 3, 1, 3)) ) ## as() show( as(co, "PeriodicBJFilter") ) show( as(co, "PeriodicSPFilter") ) ## change the sign convention: sp1 <- as(bj1, "PeriodicSPFilter") ## the two parameterisations have different signs: bj1 sp1 ## nevertheless, bj1 and sp1 represent the same filter filterPoly(bj1) filterPoly(sp1) identical(filterPoly(bj1), filterPoly(sp1)) # TRUE filterPolyCoef(bj1) filterPolyCoef(sp1) identical(filterPolyCoef(bj1), filterPolyCoef(sp1)) # TRUE filterOrder(bj1) nSeasons(bj1)## a toy filter of order c(3, 3, 3, 3) and 4 seasons co <- matrix(c(1, 1, 0, 2, 2, 2, 3, 0, 0, 4, 4, 4), nrow = 4, ncol = 3) ## these are equivalent: bj1 <- new("PeriodicBJFilter", coef = co) bj1b <- new("PeriodicBJFilter", coef = co, order = 3) bj1c <- new("PeriodicBJFilter", coef = co, order = c(3, 3, 3, 3)) identical(bj1b, bj1c) # TRUE identical(bj1, bj1b) # FALSE but only because classbj1@order is "integer" ## a more refined spec. for the order: show( new("PeriodicBJFilter", coef = co, order = c(2, 3, 1, 3)) ) ## as() show( as(co, "PeriodicBJFilter") ) show( as(co, "PeriodicSPFilter") ) ## change the sign convention: sp1 <- as(bj1, "PeriodicSPFilter") ## the two parameterisations have different signs: bj1 sp1 ## nevertheless, bj1 and sp1 represent the same filter filterPoly(bj1) filterPoly(sp1) identical(filterPoly(bj1), filterPoly(sp1)) # TRUE filterPolyCoef(bj1) filterPolyCoef(sp1) identical(filterPolyCoef(bj1), filterPolyCoef(sp1)) # TRUE filterOrder(bj1) nSeasons(bj1)
Class PeriodicFilterModel.
Objects can be created by calls of the form new("PeriodicFilterModel", pcmean, pcintercept, ...).
center:Object of class "numeric" ~~
intercept:Object of class "numeric" ~~
sigma2:Object of class "numeric" ~~
ar:Object of class "PeriodicArFilter" ~~
ma:Object of class "PeriodicMaFilter" ~~
modelCycle:Object of class "BasicCycle" ~~
Class "VirtualPeriodicFilterModel", directly.
Class "PeriodicArmaSpec", directly.
Class "PeriodicArmaFilter", by class "PeriodicArmaSpec", distance 2.
Functions with methods for this class:
signature(object = "PeriodicFilterModel"): ...
Class PeriodicIntegratedArmaSpec.
Objects can be created by calls of the form new("PeriodicIntegratedArmaSpec", ...).
pcmodel:Object of class "PeriodicArmaModel" ~~
signature(object = "PeriodicIntegratedArmaSpec"): ...
signature(object = "PeriodicIntegratedArmaSpec"): ...
Class PeriodicInterceptSpec.
Objects can be created by calls of the form new("PeriodicInterceptSpec", ...).
center:Object of class "numeric" ~~
intercept:Object of class "numeric" ~~
sigma2:Object of class "numeric" ~~
modelCycle:Object of class "BasicCycle" ~~
Class "numeric", from data part.
Class "vector", by class "numeric", distance 2.
Class "index", by class "numeric", distance 2.
Class "replValue", by class "numeric", distance 2.
Class "numLike", by class "numeric", distance 2.
Class "number", by class "numeric", distance 2.
Class "atomicVector", by class "numeric", distance 2.
signature(object = "PeriodicInterceptSpec"): ...
signature(x = "PeriodicInterceptSpec", abb = "ANY"): ...
signature(.Object = "PeriodicInterceptSpec"): ...
signature(object = "PeriodicInterceptSpec"): ...
signature(object = "PeriodicInterceptSpec"):
...
Class PeriodicMaModel.
Objects can be created by calls of the form new("PeriodicMaModel", ar, ma, sigma2, ...).
sigma2:Object of class "numeric" ~~
ar:Object of class "PeriodicArFilter" ~~
ma:Object of class "PeriodicMaFilter" ~~
center:Object of class "numeric" ~~
intercept:Object of class "numeric" ~~
modelCycle:Object of class "BasicCycle" ~~
Class "PeriodicArmaModel", directly.
Class "VirtualPeriodicArmaModel", by class "PeriodicArmaModel", distance 2.
Class "PeriodicArmaSpec", by class "PeriodicArmaModel", distance 2.
Class "VirtualPeriodicFilterModel", by class "PeriodicArmaModel", distance 3.
Class "VirtualPeriodicStationaryModel", by class "PeriodicArmaModel", distance 3.
Class "PeriodicArmaFilter", by class "PeriodicArmaModel", distance 3.
Class "VirtualPeriodicAutocovarianceModel", by class "PeriodicArmaModel", distance 4.
Class "VirtualPeriodicMeanModel", by class "PeriodicArmaModel", distance 4.
signature(object = "PeriodicMaModel"): ...
"PeriodicMTS_ts"
Class "PeriodicMTS_ts" is a periodic class holding
multivariate "ts" objects.
Objects can be created by calls of the form new("PeriodicMTS_ts", x, ...).
.Data:Object of class "vector" ~~
cycle:Object of class "BasicCycle" ~~
pcstart:Object of class "ANY" ~~
tsp:Object of class "numeric" ~~
.S3Class:Object of class "character" ~~
Class "PeriodicTimeSeries", directly.
Class "ts", directly.
Class "Cyclic", by class "PeriodicTimeSeries", distance 2.
Class "structure", by class "ts", distance 2.
Class "oldClass", by class "ts", distance 2.
Class "vector", by class "ts", distance 3, with explicit coerce.
signature(from = "ts", to = "PeriodicMTS_ts"): ...
signature(.Object = "PeriodicMTS_ts"): ...
"PeriodicMTS_zooreg"
Class "PeriodicMTS_zooreg" is a periodic class holding
multivariate "zooreg" objects.
Objects can be created by calls of the form new("PeriodicMTS_zooreg", ...).
cycle:Object of class "BasicCycle" ~~
.S3Class:Object of class "character" ~~
pcstart:Object of class "ANY" ~~
Class "PeriodicTimeSeries", directly.
Class "ts", directly.
Class "Cyclic", by class "PeriodicTimeSeries", distance 2.
Class "structure", by class "ts", distance 2.
Class "oldClass", by class "ts", distance 2.
Class "vector", by class "ts", distance 3, with explicit coerce.
No methods defined with class "PeriodicMTS_zooreg" in the signature.
"PeriodicMTS"
Class "PeriodicMTS" is the main class for multivariate periodic
time series in package "pcts".
Objects can be created by calls of the form
new("PeriodicMTS", ...) but it is recommended to use
the function pcts in most cases.
.Data:Object of class "matrix",
the core data. Several functions can be used to extract it in
various formats, see Vec.
cycle:Object of class "BasicCycle",
representing the seasonal information, see
pcCycle.
pcstart:Object of class "ANY",
the time of the first observation.
Class "PeriodicTimeSeries", directly.
Class "matrix", from data part.
Class "Cyclic", by class "PeriodicTimeSeries", distance 2.
Class "array", by class "matrix", distance 2.
Class "mMatrix", by class "matrix", distance 2.
Class "optionalMatrix", by class "matrix", distance 2.
Class "structure", by class "matrix", distance 3.
Class "vector", by class "matrix", distance 4, with explicit coerce.
signature(x = "PeriodicMTS"): ...
signature(x = "PeriodicMTS", i = "missing", j = "missing", drop = "ANY"): ...
signature(x = "PeriodicMTS", i = "ANY", j = "missing", drop = "ANY"): ...
signature(x = "PeriodicMTS", i = "ANY", j = "ANY", drop = "ANY"): ...
signature(x = "PeriodicMTS", i = "AnyDateTime", j = "missing", drop = "ANY"): ...
signature(x = "PeriodicMTS", i = "AnyDateTime", j = "ANY", drop = "ANY"): ...
signature(x = "PeriodicMTS", i = "ANY", j = "ANY"): ...
signature(from = "mts", to = "PeriodicMTS"): ...
signature(from = "PeriodicMTS", to = "ts"): ...
signature(from = "ts", to = "PeriodicMTS"): ...
signature(from = "PeriodicMTS", to = "Cyclic"): ...
signature(from = "PeriodicMTS", to = "Cyclic"): ...
signature(x = "PeriodicMTS", y = "missing"): ...
signature(object = "PeriodicMTS"): ...
signature(object = "PeriodicMTS"): ...
signature(model = "PeriodicArModel", x = "PeriodicMTS"): ...
signature(object = "PeriodicMTS"): ...
signature(object = "PeriodicMTS"): ...
class PeriodicTS (univariate periodic time series),
pcts (create periodic time series),
dataFranses1996 and pcts-package for examples
pcfr <- pcts(dataFranses1996) colnames(pcfr)[4] # "GermanyGNP" ## extracting single time series as univariate class(pcfr[[4]]) # "PeriodicTS" identical(pcfr[[4]], pcfr$GermanyGNP ) # TRUE identical(pcfr[[4]], pcfr[["GermanyGNP"]]) # TRUE plot(pcfr[[4]]) ## ... and as multivariate pcfr[4] # "PeriodicMTS" plot(pcfr[4]) ## extracting more than one time series plot(pcfr[2:4]) summary(pcfr[2:4]) pcfr2 <- pcfr[[2]] plot(pcfr2)pcfr <- pcts(dataFranses1996) colnames(pcfr)[4] # "GermanyGNP" ## extracting single time series as univariate class(pcfr[[4]]) # "PeriodicTS" identical(pcfr[[4]], pcfr$GermanyGNP ) # TRUE identical(pcfr[[4]], pcfr[["GermanyGNP"]]) # TRUE plot(pcfr[[4]]) ## ... and as multivariate pcfr[4] # "PeriodicMTS" plot(pcfr[4]) ## extracting more than one time series plot(pcfr[2:4]) summary(pcfr[2:4]) pcfr2 <- pcfr[[2]] plot(pcfr2)
A class for filters following the signal processing sign convention.
Objects can be created by calls of the form new("PeriodicSPFilter", coef, order, ...).
coef:Object of class "matrix" ~~
order:Object of class "numeric" ~~
Class "PeriodicMonicFilterSpec", directly.
Class "VirtualSPFilter", directly.
Class "VirtualMonicFilterSpec", by class "PeriodicMonicFilterSpec", distance 2.
Class "VirtualMonicFilter", by class "VirtualSPFilter", distance 2.
signature(from = "matrix", to = "PeriodicSPFilter"): ...
signature(from = "PeriodicBJFilter", to = "PeriodicSPFilter"): ...
signature(from = "PeriodicSPFilter", to = "PeriodicBJFilter"): ...
signature(object = "PeriodicSPFilter", convention = "character"): ...
signature(object = "PeriodicSPFilter"): ...
signature(object = "PeriodicSPFilter"): ...
signature(object = "PeriodicSPFilter"): ...
Georgi N. Boshnakov
## see "PeriodicBJFilter-class" for examples## see "PeriodicBJFilter-class" for examples
Class PeriodicTimeSeries.
A virtual Class: No objects may be created from it.
PeriodicTimeSeries is the root class for the periodic time
series classes in package "pcts". It can be used in signatures
for methods that can handle objcets from any of them.
cycle:Object of class "BasicCycle".
pcstart:Object of class "ANY".
Class "Cyclic", directly.
signature(x = "PeriodicTimeSeries"): ...
signature(x = "PeriodicTimeSeries"): ...
signature(x = "PeriodicTimeSeries", maxlag = "ANY", lag_0 = "missing"): ...
signature(x = "PeriodicTimeSeries", nullmodel = "character"): ...
signature(x = "PeriodicTimeSeries"): ...
signature(x = "PeriodicTimeSeries"): ...
signature(x = "PeriodicTimeSeries", type = "character"): ...
signature(x = "PeriodicTimeSeries", type =
"missing"): ...
signature(x = "PeriodicTimeSeries"): ...
classes PeriodicTS, PeriodicMTS
"PeriodicTS_ts"
Class "PeriodicTS_ts" is a periodic class holding
"ts" objects.
Objects can be created by calls of the form new("PeriodicTS_zooreg", ...).
Objects can be created by calls of the form new("PeriodicTS_ts", x, ...).
.Data:Object of class "vector" ~~
cycle:Object of class "BasicCycle" ~~
tsp:Object of class "numeric" ~~
.S3Class:Object of class "character" ~~
pcstart:Object of class "ANY" ~~
Class "PeriodicTimeSeries", directly.
Class "ts", directly.
Class "Cyclic", by class "PeriodicTimeSeries", distance 2.
Class "structure", by class "ts", distance 2.
Class "oldClass", by class "ts", distance 2.
Class "vector", by class "ts", distance 3, with explicit coerce.
signature(from = "ts", to = "PeriodicTS_ts"): ...
signature(.Object = "PeriodicTS_ts"): ...
"PeriodicTS_zooreg"
Class "PeriodicTS_zooreg" is a periodic class holding
"zooreg" objects.
Objects can be created by calls of the form new("PeriodicTS_zooreg", ...).
cycle:Object of class "BasicCycle" ~~
.S3Class:Object of class "character" ~~
pcstart:Object of class "ANY" ~~
Class "PeriodicTimeSeries", directly.
Class "ts", directly.
Class "Cyclic", by class "PeriodicTimeSeries", distance 2.
Class "structure", by class "ts", distance 2.
Class "oldClass", by class "ts", distance 2.
Class "vector", by class "ts", distance 3, with explicit coerce.
No methods defined with class "PeriodicTS_zooreg" in the signature.
classes PeriodicTS and
PeriodicMTS
"PeriodicTS"
Class "PeriodicTS" is the main class for univariate periodic
time series in package "pcts".
Objects can be created from numeric vectors and objects from other
time series classes by calling pcts (recommended in most
cases).
It is possible also to use calls of the form new("PeriodicTS",
...). This is more useful in programming.
.Data:Object of class "numeric",
the core data. Several functions can be used to extract it in
various formats, see Vec.
cycle:Object of class "BasicCycle",
representing the seasonal information, see
pcCycle.
pcstart:Object of class "ANY",
the time of the first observation.
Class "PeriodicTimeSeries", directly.
Class "numeric", from data part.
Class "Cyclic", by class "PeriodicTimeSeries", distance 2.
Class "vector", by class "numeric", distance 2.
Class "index", by class "numeric", distance 2.
Class "replValue", by class "numeric", distance 2.
Class "numLike", by class "numeric", distance 2.
Class "number", by class "numeric", distance 2.
Class "atomicVector", by class "numeric", distance 2.
Class "numericVector", by class "numeric", distance 2.
Class "replValueSp", by class "numeric", distance 3.
Class "Mnumeric", by class "numeric", distance 3.
signature(x = "PeriodicTS", i = "AnyDateTime", j = "missing", drop = "ANY"): ...
signature(x = "PeriodicTS", i = "missing", j = "missing", drop = "ANY"): ...
signature(from = "mts", to = "PeriodicTS"): ...
signature(from = "PeriodicTS", to = "ts"): ...
signature(from = "ts", to = "PeriodicTS"): ...
signature(from = "PeriodicTS", to = "Cyclic"): ...
signature(from = "PeriodicTS", to = "Cyclic"): ...
signature(x = "PeriodicTS", y = "missing"): ...
signature(object = "PeriodicTS"): ...
signature(object = "PeriodicTS"): ...
signature(x = "PeriodicTS", maxlag = "ANY"): ...
signature(model = "PeriodicArModel", x = "PeriodicTS"): ...
signature(object = "PeriodicTS"): ...
signature(object = "PeriodicTS"): ...
pcts for creating "PeriodicTS" objects from raw
vectors and objects from other time series classes.
PeriodicMTS for multivariate periodic time
series.
Objects and methods for class PeriodicVector.
PeriodicVector(x, period = length(x))PeriodicVector(x, period = length(x))
x |
the values for inidices from 1 to |
period |
the period, defaults to |
A -periodic vector, , is such that
for any integers .
Class PeriodicVector stores the values of
and provides indexing methods for extracting and setting its
elements.
an object from class "PeriodicVector"
Objects can be created by calls of the form new("PeriodicVector", ...)
or more conveniently by using "PeriodicVector()".
.Data:Object of class "numeric" ~~
period:Object of class "numeric" ~~
Class "numeric", from data part.
Class "vector", by class "numeric", distance 2.
Class "atomicVector", by class "numeric", distance 2.
Class "index", by class "numeric", distance 2.
Class "numLike", by class "numeric", distance 2.
Class "number", by class "numeric", distance 2.
Class "replValue", by class "numeric", distance 2.
"PeriodicVector" methods are defined for "[" and
"[<-". Arithmetic operations just inherit the recycling rules
from "numeric".
signature(x = "PeriodicVector", i = "ANY", j = "ANY", drop = "ANY"): ...
signature(x = "PeriodicVector", i = "ANY", j = "missing", drop = "ANY"): ...
signature(x = "PeriodicVector", i = "missing", j = "ANY", drop = "ANY"): ...
signature(x = "PeriodicVector", i = "missing", j = "missing", drop = "ANY"): ...
signature(x = "PeriodicVector", i = "ANY", j = "ANY", value = "ANY"): ...
signature(x = "PeriodicVector", i = "missing", j = "ANY", value = "ANY"): ...
Georgi N. Boshnakov
PeriodicVector(1:4, period = 4) PeriodicVector(1:4) ## same new("PeriodicVector", 1:4, period = 4) ## if period is given but x is missing, the vector is filled with NA's PeriodicVector(period = 4) ## this throws error, since length(x) != period: ## PeriodicVector(1:3, period = 4) ## extract x <- PeriodicVector(1:4) x[3:12] x[c(3, 7, 11, 15)] # any indices in (-Inf, Inf) work x[0] x[-3:0] ## "[<-" works on the underling vector x[1] <- 11; x ## modulo indexing works also in assignments: x[5] <- 21; x ## empty index returns the underlying vector x[] ## the recycling rule applies on assignment x[] <- 9; x x[] <- 1:2; x ## this gives warning, as for numeric vectors ## x[] <- 8:1 ## compare: ## x <- 1:4 ## x[] <- 8:1 ## arithmetic works as usual: 2 * x x + 1:4 ## x + 1:3 # warning - '... a multiple ...'PeriodicVector(1:4, period = 4) PeriodicVector(1:4) ## same new("PeriodicVector", 1:4, period = 4) ## if period is given but x is missing, the vector is filled with NA's PeriodicVector(period = 4) ## this throws error, since length(x) != period: ## PeriodicVector(1:3, period = 4) ## extract x <- PeriodicVector(1:4) x[3:12] x[c(3, 7, 11, 15)] # any indices in (-Inf, Inf) work x[0] x[-3:0] ## "[<-" works on the underling vector x[1] <- 11; x ## modulo indexing works also in assignments: x[5] <- 21; x ## empty index returns the underlying vector x[] ## the recycling rule applies on assignment x[] <- 9; x x[] <- 1:2; x ## this gives warning, as for numeric vectors ## x[] <- 8:1 ## compare: ## x <- 1:4 ## x[] <- 8:1 ## arithmetic works as usual: 2 * x x + 1:4 ## x + 1:3 # warning - '... a multiple ...'
Convert a periodic mean to periodic intercept and vice versa.
permean2intercept(mean, coef, order, nseasons = nrow(coef)) intercept2permean(intercept, coef, order, nseasons = nrow(coef))permean2intercept(mean, coef, order, nseasons = nrow(coef)) intercept2permean(intercept, coef, order, nseasons = nrow(coef))
mean |
periodic mean, numeric. |
coef |
PAR coefficients, matrix. |
order |
PAR order, vector of positive integers. |
nseasons |
number of seasons, a.k.a. period. |
intercept |
periodic intercepts, numeric. |
A PAR model can be written in mean corrected or intercept form.
permean2intercept calculates the intercepts from the means,
while intercept2permean does the inverse (means from
intercepts).
No check is made for periodic stationarity of the model. Converting from mean corrected to intercept form allways succeeds and in fact the means do not need to be means. In the opposite direction there may be problems due to unit roots and similar features.
a numeric vector
Georgi N. Boshnakov
mu <- c(1, 2) pm1 <- PeriodicArModel(matrix(c(0.5, 0.5), nrow = 2), order = rep(1, 2), sigma2 = 1, mean = mu) cc <- permean2intercept(mu, pm1@ar@coef, c(1,1)) cc intercept2permean(cc, pm1@ar@coef, c(1,1)) d <- 4 mu <- 1:d co <- rep(0.5, d) pm1 <- PeriodicArModel(matrix(co, nrow = d), order = rep(1, d), sigma2 = 1, mean = mu) cc <- permean2intercept(mu, pm1@ar@coef, order = rep(1, d)) cc intercept2permean(cc, pm1@ar@coef, order = rep(1, d) )mu <- c(1, 2) pm1 <- PeriodicArModel(matrix(c(0.5, 0.5), nrow = 2), order = rep(1, 2), sigma2 = 1, mean = mu) cc <- permean2intercept(mu, pm1@ar@coef, c(1,1)) cc intercept2permean(cc, pm1@ar@coef, c(1,1)) d <- 4 mu <- 1:d co <- rep(0.5, d) pm1 <- PeriodicArModel(matrix(co, nrow = d), order = rep(1, d), sigma2 = 1, mean = mu) cc <- permean2intercept(mu, pm1@ar@coef, order = rep(1, d)) cc intercept2permean(cc, pm1@ar@coef, order = rep(1, d) )
Compute the multi-companion form of a per model.
permodelmf(permodel, update = TRUE)permodelmf(permodel, update = TRUE)
permodel |
a model. |
update |
If TRUE store the multi-companion form in
|
todo:
the multi-companion form of the model or the updated model, as described in Details.
Georgi N. Boshnakov
Boshnakov GN, Iqelan BM (2009). “Generation of time series models with given spectral properties.” J. Time Series Anal., 30(3), 349–368. ISSN 0143-9782, doi:10.1111/j.1467-9892.2009.00617.x.
Convert PIAR coefficients to PAR coefficients
pi1ar2par(picoef, parcoef) piar2par(picoef, parcoef)pi1ar2par(picoef, parcoef) piar2par(picoef, parcoef)
picoef |
coefficients of the periodic integration filter, a numeric vector or matrix, see Details. |
parcoef |
coefficients of the periodically correlated part of the model. |
These functions expand periodic filters represented in multiplicative
form. The non-periodic analogue of the operation of these functions
is representing a multiplicative filter like , where
is the backward shift operator, by the single filter , which is just a product of the polynomials,
and .
In the non-periodic case however this operation is not, in general, equivalent to multiplication of the corresponding polynomials. It is also not commutative.
pi1ar2par converts PIAR(1) model coefficients specified as a
set of coefficients corresponding to a periodic unit root and PAR
coefficients to coefficients for a single filter.
piar2par does the same but admits higher order periodic
integration.
picoef is a matrix, specifying one or more first order periodic
unit root filters. Each column contains the coefficients of one
filter. If there is only one filter, its coefficients can be given as
a numeric vector.
The filters are applied from right to left, in the sense that first the PAR filter is applied to the time series, then the filter specified by the last column and so on.
a matrix, whose i-th row contains the coefficients for the i-th season.
Georgi N. Boshnakov
## Lina's example parcoef <- rbind(c(0.5, -0.06), c(0.6, -0.08), c(0.7, -0.1), c(0.2, 0.15) ) picoef1 <- c(0.8, 1.25, 2, 0.5) parcoef2 <- pi1ar2par(picoef1, parcoef) picoef2 <- c(4, 0.25, 5, 0.2) coefper2I2 <- pi1ar2par(picoef2, parcoef2)## Lina's example parcoef <- rbind(c(0.5, -0.06), c(0.6, -0.08), c(0.7, -0.1), c(0.2, 0.15) ) picoef1 <- c(0.8, 1.25, 2, 0.5) parcoef2 <- pi1ar2par(picoef1, parcoef) picoef2 <- c(4, 0.25, 5, 0.2) coefper2I2 <- pi1ar2par(picoef2, parcoef2)
Class PiPeriodicArmaModel.
Objects can be created by calls of the form new("PiPeriodicArmaModel", ...).
piorder:Object of class "numeric" ~~
picoef:Object of class "matrix" ~~
pcmodel:Object of class "PeriodicArmaModel" ~~
Class "VirtualPeriodicFilterModel", directly.
Class "PeriodicIntegratedArmaSpec", directly.
signature(object = "PiPeriodicArmaModel"): ...
Class PiPeriodicArModel.
Objects can be created by calls of the form new("PiPeriodicArModel", ...).
piorder:Object of class "numeric" ~~
picoef:Object of class "matrix" ~~
pcmodel:Object of class "PeriodicArmaModel" ~~
Class "PiPeriodicArmaModel", directly.
Class "VirtualPeriodicFilterModel", by class "PiPeriodicArmaModel", distance 2.
Class "PeriodicIntegratedArmaSpec", by class "PiPeriodicArmaModel", distance 2.
signature(x = "ANY", model = "PiPeriodicArModel"): ...
signature(model = "PiPeriodicArModel", x = "ANY"): ...
signature(object = "PiPeriodicArModel"): ...
Class PiPeriodicMaModel.
Objects can be created by calls of the form new("PiPeriodicMaModel", ...).
piorder:Object of class "numeric" ~~
picoef:Object of class "matrix" ~~
pcmodel:Object of class "PeriodicArmaModel" ~~
Class "PiPeriodicArmaModel", directly.
Class "VirtualPeriodicFilterModel", by class "PiPeriodicArmaModel", distance 2.
Class "PeriodicIntegratedArmaSpec", by class "PiPeriodicArmaModel", distance 2.
No methods defined with class "PiPeriodicMaModel" in the signature.
Compute the McLeod-Ljung-Box test statistic for examining the null hypothesis of periodic white noise.
pwn_McLeodLjungBox_test(acf, nepoch, use = 1:maxlag, maxlag = ncol(as.matrix(acf)) - 1, period = nrow(as.matrix(acf)), fitdf = numeric(period))pwn_McLeodLjungBox_test(acf, nepoch, use = 1:maxlag, maxlag = ncol(as.matrix(acf)) - 1, period = nrow(as.matrix(acf)), fitdf = numeric(period))
acf |
the sample periodic autocorrelation function of the time series. |
nepoch |
number of cycles used in computing the acf. |
use |
number of lags to use, may be a vector. |
maxlag |
maximal lag. |
period |
number of seasons in a cycle. |
fitdf |
degrees of freedom corrections for the number of estimated parameters, see Details. |
The McLeod-Ljung-Box test can be used to test the null hypothesis of periodic white noise.
If acf contains sample autocorrelations of residuals from a
fitted model, a correction of the degrees of freedom is strongly
recommended.
Argument fitdf is a vector specifying how may degrees of
freedom to subtract for each season. In the case of PAR models
fitdf can be set to the PAR orders.
The value of the statistic is set to NA where the correction for degrees of freedom results in negative numbers.
A list containing the following components:
statistic |
the value of the test statistic for each lag
specified by |
df |
the corresponding degrees of freedom |
TODO: Consolidate this and similar tests!
There is a typo in McLeod (1994), eq. (4.5), noted by (McLeod 1995).
Georgi N. Boshnakov
McLeod AI (1994).
“Diagnostic checking of periodic autoregression models with application.”
Journal of Time Series Analysis, 15(2), 221–233.
McLeod AI (1995).
“Diagnostic checking of periodic autoregression models with application.”
Journal of Time Series Analysis, 16(6), 647-648.
doi:10.1111/j.1467-9892.1995.tb00260.x, This corrects some typos in the eponimous article McLeod (1994).
Box.test for the non-periodic case
Class SamplePeriodicAutocorrelations.
Objects can be created by calls of the form new("SamplePeriodicAutocorrelations", ..., data).
modelCycle:Object of class "BasicCycle" ~~
data:Object of class "Lagged" ~~
n:Object of class "numeric" ~~
varnames:Object of class "character" ~~
objectname:Object of class "character" ~~
Class "PeriodicAutocorrelations", directly.
Class "Fitted", directly.
Class "ModelCycleSpec", by class "PeriodicAutocorrelations", distance 2.
Class "FlexibleLagged", by class "PeriodicAutocorrelations", distance 2.
Class "VirtualPeriodicAutocorrelations", by class "PeriodicAutocorrelations", distance 2.
Class "Lagged", by class "PeriodicAutocorrelations", distance 3.
Class "VirtualPeriodicModel", by class "PeriodicAutocorrelations", distance 3.
No methods defined with class "SamplePeriodicAutocorrelations" in the signature.
Class SamplePeriodicAutocovariances.
Objects can be created by calls of the form new("SamplePeriodicAutocovariances", ..., data).
modelCycle:Object of class "BasicCycle" ~~
data:Object of class "Lagged" ~~
n:Object of class "numeric" ~~
varnames:Object of class "character" ~~
objectname:Object of class "character" ~~
Class "PeriodicAutocovariances", directly.
Class "Fitted", directly.
Class "ModelCycleSpec", by class "PeriodicAutocovariances", distance 2.
Class "FlexibleLagged", by class "PeriodicAutocovariances", distance 2.
Class "VirtualPeriodicAutocovariances", by class "PeriodicAutocovariances", distance 2.
Class "Lagged", by class "PeriodicAutocovariances", distance 3.
Class "VirtualPeriodicModel", by class "PeriodicAutocovariances", distance 3.
signature(x = "SamplePeriodicAutocovariances", maxlag = "ANY", lag_0 = "missing"): ...
Methods for seqSeasons() in package pcts.
signature(x = "BasicCycle")signature(x = "Cyclic")signature(x = "VirtualPeriodicModel")allSeasons for related functions and examples
sigmaSq in package pctsMethods for sigmaSq in package pcts.
signature(object = "PeriodicIntegratedArmaSpec")signature(object = "PeriodicInterceptSpec")Select randomly a periodic autoregression model and return the periodic autocovariances associated with it.
sim_parAcvf(period, order, sigma2)sim_parAcvf(period, order, sigma2)
period |
the period, a positive integer. |
order |
the AR order, a vector of non-negative integers. |
sigma2 |
the variances of the innovations, a numeric vector of
length |
Uses sim_parCoef() to generate a random PAR model.
an object of class "matrix". In addition, the specification of the
model is in attribute "model" which is a list with the
following components:
ar |
a matrix, the coefficients of the PAR model, |
sigma2 |
numeric, the innovation variances, |
order |
the PAR order. |
Georgi N. Boshnakov
Boshnakov GN, Iqelan BM (2009). “Generation of time series models with given spectral properties.” J. Time Series Anal., 30(3), 349–368. ISSN 0143-9782, doi:10.1111/j.1467-9892.2009.00617.x.
sim_parAcvf(2, 5) sim_parAcvf(3, 5) res <- sim_parAcvf(2, 6) res slMatrix(res)[3, 4, type = "tt"] res <- sim_parAcvf(2, 4) attr(res, "model") acv <- res[ , ] # drop attributes acv[2, 1 + 0] acv[2, 1 + 1] slMatrix(acv)[2, 0] slMatrix(acv)[2, 1] slMatrix(acv)[3, 4, type = "tt"] slMatrix(acv)[1:2, 1:2, type = "tt"] slMatrix(acv)[1:4, 1:4, type = "tt"] ## TODO: need method for autocorrelation() ## pc.acrf(acv) ## TODO: these need changing, after the change of the return values of sim_parAcvf ## pc.fcoeffs(acv, 2) ## pc.fcoeffs(acv, 3) ## pc.fcoeffs(acv, 4) pcts:::calc_predictionCoefficients(acv, c(2, 2)) pcts:::calc_predictionCoefficients(acv, c(3, 3)) pcts:::calc_predictionCoefficients(acv, c(4, 4))sim_parAcvf(2, 5) sim_parAcvf(3, 5) res <- sim_parAcvf(2, 6) res slMatrix(res)[3, 4, type = "tt"] res <- sim_parAcvf(2, 4) attr(res, "model") acv <- res[ , ] # drop attributes acv[2, 1 + 0] acv[2, 1 + 1] slMatrix(acv)[2, 0] slMatrix(acv)[2, 1] slMatrix(acv)[3, 4, type = "tt"] slMatrix(acv)[1:2, 1:2, type = "tt"] slMatrix(acv)[1:4, 1:4, type = "tt"] ## TODO: need method for autocorrelation() ## pc.acrf(acv) ## TODO: these need changing, after the change of the return values of sim_parAcvf ## pc.fcoeffs(acv, 2) ## pc.fcoeffs(acv, 3) ## pc.fcoeffs(acv, 4) pcts:::calc_predictionCoefficients(acv, c(2, 2)) pcts:::calc_predictionCoefficients(acv, c(3, 3)) pcts:::calc_predictionCoefficients(acv, c(4, 4))
Generate a periodic autoregression model, possibly integrated.
sim_parCoef(period, n.root, sigma2 = rep(1, period), ...)sim_parCoef(period, n.root, sigma2 = rep(1, period), ...)
period |
number of seasons in a cycle. |
n.root |
number of non-zero roots, see details. |
sigma2 |
variances of the innovations. |
... |
additional arguments to be passed down to |
sim_parCoef uses the multi-companion method to generate the
model. The function is essentially a wrapper for sim_pcfilter.
The order of the filter is set to n.root for each season. Part
of the spectral information may be specified with the "..."
arguments, see sim_pcfilter and sim_mc for
a discussion of this.
a periodic autoregression model as a list with elements:
ar |
a matrix whose |
sigma2 |
the innovation variances, a numeric vector. |
Georgi N. Boshnakov
Boshnakov GN, Iqelan BM (2009). “Generation of time series models with given spectral properties.” J. Time Series Anal., 30(3), 349–368. ISSN 0143-9782, doi:10.1111/j.1467-9892.2009.00617.x.
sim_parCoef(2, 4) # 2 seasons sim_parCoef(2, 4, sigma2 = c(2, 4)) sim_parCoef(2, 1) sim_parCoef(4, 2) # 4 seasons sim_parCoef(period = 4, n.root = 6, eigabs = c(1, 1, 1, 0.036568887, 0.001968887), type.eigval = c("cp", "r", "r", "r", "r"), eigsign = c(pi/2, 1, -1, 1, -1))sim_parCoef(2, 4) # 2 seasons sim_parCoef(2, 4, sigma2 = c(2, 4)) sim_parCoef(2, 1) sim_parCoef(4, 2) # 4 seasons sim_parCoef(period = 4, n.root = 6, eigabs = c(1, 1, 1, 0.036568887, 0.001968887), type.eigval = c("cp", "r", "r", "r", "r"), eigsign = c(pi/2, 1, -1, 1, -1))
Simulate a realization of a periodically correlated arma model or a continuation of an existing series. Initial values may be given too.
sim_pc(model, n = NA, randgen = rnorm, seasonof1st = 1, nepochs = NA, n.start = NA, x, eps, nmean = NULL, nintercept = NULL, ...)sim_pc(model, n = NA, randgen = rnorm, seasonof1st = 1, nepochs = NA, n.start = NA, x, eps, nmean = NULL, nintercept = NULL, ...)
model |
a list with elements
|
n |
length of the series. |
randgen |
random number generator as required by
|
seasonof1st |
season of the first value. |
nepochs |
number of epochs; if |
n.start |
burn-in number; generate |
x |
initial or before values, see Details. |
eps |
innovations, see Details. |
nmean |
a vector of length |
nintercept |
a vector of length |
... |
any additional arguments to be passed on to |
Argument x can be used to specify two types of initialisation
values - ‘before’ and ‘init’. They are used similarly in computations
but ‘before’ values are not included in the result, while ‘init’
values are (unless dropped due to n.start). ‘Before’ values
provide a convenient way to simulate continuation trajectories for a
time series, for example for simulation based prediction intervals.
If x is "numeric", it represents ‘before’
values. Alternatively, x can be a list with components
"before" and "init".
Innovations are usually generated with the random number generator
specified by randgen (with default rnorm) and the
... parameters by a call to the function sim_pwn, see
the documentation for sim_pwn for various ways to control the
distribution of the generated sequence.
The innovations can also be generated in advance and supplied using
argument eps. If eps is numeric, it is taken to
represent the innovations. Alternatively, eps can be a list
with the innovations in component "main". This list may also
contain components "before" and/or "init" specifying
‘before’ or ‘initial’ values, with interpretation as for x.
nintercept can be used to specify trend representing the effect
of time and/or covariates. As for eps, if it is numeric it is
taken to represent the main values. It can also be a list with
components before, init, and main.
To avoid ambiguity, let's reiterate that before values are past
values of the corresponding quantity (before the start of the
simulated series), while init values are "initial" values. In
particular, if initial values are specified for x, these will
form the start of the generated series (unless n.start leads to
them being discarded).
If before values are specified for the series and the innovations, then they play a role analogous to that of initial values, so it does not make much sense to supply also initial values.
The function effectively does the following.
innov is generated if not supplied,
a vector of innovations is created
eps <- c(innovbefore,innovinit,innov),
a vector x is created of the same length as eps,
and initialised with xbefore and xinit.
If there are no initial or before values, these are assumed to be 0.
The remaining values of x are filled using the pc-arma equations.
Finally, the xbefore values are discarded as well as the first
n.start values.
n.start should usually be a multiple of the period since
otherwise the first observation in the returned vector will not
correspond to seasonof1st.
sim_pc deals mainly with the interpretation of the parameters.
The actual computations are done by pc.filter. Moreover,
sim_pc does not look at the model. It knows only about
model$period and uses it to compute n if n is not
specified.
(It probably should not care even about this.)
numeric, the simulated time series
option to return the innovation sequence; option to include the before values.
option to return the season of the first value in the returned series
(it may be different from seasonof1st due to n.start).
Georgi N. Boshnakov
m1 <- rbind( c(1, 0.81, 0), c(1, 0.4972376, 0.4972376) ) testphi <- slMatrix( init = m1 ) m2 <- rbind( c(1, 0, 0), c(1, 0, 0) ) testtheta <- slMatrix( init = m2 ) ## phi and theta are slMatrix here. mo1 <- list(phi = testphi, theta = testtheta, p = 2, q = 2, period = 2) set.seed(1234) a1 <- sim_pc(mo1, 100) ## phi and theta are ordinary matrices here. mo2 <- list(phi = m1[ , 2:ncol(m1)], theta = m2[ , 2:ncol(m2)], p = 2, q = 2, period = 2) set.seed(1234) a2 <- sim_pc(mo2, 100) identical(a1, a2) ## Lina's PAR model parcoef <- rbind(c(0.5, -0.06), c(0.6, -0.08), c(0.7, -0.1), c(0.2, 0.15) ) picoef1 <- c(0.8, 1.25, 2, 0.5) parcoef2 <- pi1ar2par(picoef1, parcoef) picoef2 <- c(4, 0.25, 5, 0.2) coefper2I2 <- pi1ar2par(picoef2, parcoef2) #### specify the model using multi-companion approach mc2I2 <- mcompanion::mc_from_filter(coefper2I2) co2I2 <- eigen(mc2I2)$vectors co2I2 m2I2 <- mcompanion::sim_pcfilter(period = 4, n.root = 4, eigabs = c(1, 0.036568887, 0.001968887), eigsign = c(1, 1, -1), len.block = c(2, 1, 1), type.eigval = c("r", "r", "r"), co = cbind(co2I2[ ,1], rep(NA, 4), co2I2[,3:4])) m2I2$pcfilter perunit2mc <- sim_pc(list(phi = m2I2$pcfilter, p = 4, q = 0, period = 4), 500) plot(perunit2mc) plot(perunit2mc, type = "p") # todo: give example with sigmat^2 !!!m1 <- rbind( c(1, 0.81, 0), c(1, 0.4972376, 0.4972376) ) testphi <- slMatrix( init = m1 ) m2 <- rbind( c(1, 0, 0), c(1, 0, 0) ) testtheta <- slMatrix( init = m2 ) ## phi and theta are slMatrix here. mo1 <- list(phi = testphi, theta = testtheta, p = 2, q = 2, period = 2) set.seed(1234) a1 <- sim_pc(mo1, 100) ## phi and theta are ordinary matrices here. mo2 <- list(phi = m1[ , 2:ncol(m1)], theta = m2[ , 2:ncol(m2)], p = 2, q = 2, period = 2) set.seed(1234) a2 <- sim_pc(mo2, 100) identical(a1, a2) ## Lina's PAR model parcoef <- rbind(c(0.5, -0.06), c(0.6, -0.08), c(0.7, -0.1), c(0.2, 0.15) ) picoef1 <- c(0.8, 1.25, 2, 0.5) parcoef2 <- pi1ar2par(picoef1, parcoef) picoef2 <- c(4, 0.25, 5, 0.2) coefper2I2 <- pi1ar2par(picoef2, parcoef2) #### specify the model using multi-companion approach mc2I2 <- mcompanion::mc_from_filter(coefper2I2) co2I2 <- eigen(mc2I2)$vectors co2I2 m2I2 <- mcompanion::sim_pcfilter(period = 4, n.root = 4, eigabs = c(1, 0.036568887, 0.001968887), eigsign = c(1, 1, -1), len.block = c(2, 1, 1), type.eigval = c("r", "r", "r"), co = cbind(co2I2[ ,1], rep(NA, 4), co2I2[,3:4])) m2I2$pcfilter perunit2mc <- sim_pc(list(phi = m2I2$pcfilter, p = 4, q = 0, period = 4), 500) plot(perunit2mc) plot(perunit2mc, type = "p") # todo: give example with sigmat^2 !!!
Simulate periodic white noise.
sim_pwn(n = 100, period = NA, seasonof1st = 1, scale = NULL, shift = NULL, f = rnorm, ...)sim_pwn(n = 100, period = NA, seasonof1st = 1, scale = NULL, shift = NULL, f = rnorm, ...)
n |
length of the generated sample. |
period |
number of seasons in an epoch. |
seasonof1st |
season of the first observation in the result. |
scale |
scale the series by this amount, a vector of length |
shift |
shift the series by this amount, a vector of length |
f |
a function or list of functions to generate random numbers. |
... |
arguments for the random number generator(s) specified by |
First a series, say , of random numbers is generated as
requested by the argument f. Then, if shift and/or
scale are supplied, the values are modified as follows:
where is the season corresponding to time .
The vector is returned.
If f is a single a function (or name of a function), then the
series is generated (effectively) by the call f(n,...).
The argument f may also be a list whose th element
is itself a list specifying the random number generator for the
th season. The first element being the function (such as
rnorm) and the remaining elements being parameters for that
function. Parameters common to all seasons may be supplied through
the ... argument.
The argument period may be omitted. In that case it is inferred
from f and/or the lengths of shift and
scale. Currently there is no check for consistency here.
The arguments shift and scale may be used to specify
simple linear transformations of the generated values, possibly
different for the different seasons. Each of them should be a vector
of length period or one.
seasonof1st can be used to request the simulated time series to
start from a season other than the first one. Note that whatever the
value of seasonof1st, the first elements of scale,
shift and f (if a list) are taken to refer to season
one.
A vector of length representing a realization of a periodic
white noise series. The season of the first observation is
seasonof1st.
0 (base)
Georgi N. Boshnakov
## three equivalent ways to specify periodic white noise with ## normal innovatios, 2 seasons, s.d. = 0.5 for season 1, and 2 for season 2 sim_pwn(100, f = rnorm, scale = c(0.5, 2)) sim_pwn(n = 100, scale = c(0.5, 2)) # rnorm is the default generator sim_pwn(100, f = list(c(rnorm, 0, 0.5), c(rnorm, 0, 2)))## three equivalent ways to specify periodic white noise with ## normal innovatios, 2 seasons, s.d. = 0.5 for season 1, and 2 for season 2 sim_pwn(100, f = rnorm, scale = c(0.5, 2)) sim_pwn(n = 100, scale = c(0.5, 2)) # rnorm is the default generator sim_pwn(100, f = list(c(rnorm, 0, 0.5), c(rnorm, 0, 2)))
Class SimpleCycle.
Objects can be created by calls of the form new("SimpleCycle",
nseasons, seasons, first).
In addition to number of seasons, class "SimpleCycle" holds
also seasons' names and the index of the season to be treated as the
first in a cycle.
seasons:Object of class "character",
the names of the seasons.
nseasons:Object of class "integer",
number of seasons.
cycle:Object of class "character" ~~
season:Object of class "character" ~~
abbreviated:Object of class "character" ~~
Class "BareCycle", directly.
Class "BasicCycle", directly.
signature(x = "SimpleCycle", abb = "ANY"): ...
signature(x = "SimpleCycle"): ...
signature(from = "BareCycle", to = "SimpleCycle"): ...
signature(from = "BuiltinCycle", to = "SimpleCycle"): ...
signature(.Object = "SimpleCycle"): ...
signature(object = "SimpleCycle"): ...
signature(x = "SimpleCycle"): ...
signature(x = "SimpleCycle"): ...
signature(x = "SimpleCycle"): ...
signature(x = "SimpleCycle"): ...
Georgi N. Boshnakov
pcCycle for creation of cycle objects and extraction of
cycle part of time series,
BuiltinCycle-class,
SimpleCycle-class,
DayWeekCycle-class,
MonthYearCycle-class,
OpenCloseCycle-class,
QuarterYearCycle-class,
PartialCycle-class
BasicCycle-class (virtual, for use in signatures)
showClass("SimpleCycle")showClass("SimpleCycle")
Class SiPeriodicArmaModel.
Objects can be created by calls of the form new("SiPeriodicArmaModel", ...).
iorder:Object of class "numeric" ~~
siorder:Object of class "numeric" ~~
pcmodel:Object of class "PeriodicArmaModel" ~~
Class "VirtualPeriodicFilterModel", directly.
Class "PeriodicIntegratedArmaSpec", directly.
No methods defined with class "SiPeriodicArmaModel" in the signature.
Class SiPeriodicArModel.
Objects can be created by calls of the form new("SiPeriodicArModel", ...).
iorder:Object of class "numeric" ~~
siorder:Object of class "numeric" ~~
pcmodel:Object of class "PeriodicArmaModel" ~~
Class "SiPeriodicArmaModel", directly.
Class "VirtualPeriodicFilterModel", by class "SiPeriodicArmaModel", distance 2.
Class "PeriodicIntegratedArmaSpec", by class "SiPeriodicArmaModel", distance 2.
signature(model = "SiPeriodicArModel", x = "ANY"): ...
signature(object = "SiPeriodicArModel"): ...
Class SiPeriodicMaModel.
Objects can be created by calls of the form new("SiPeriodicMaModel", ...).
iorder:Object of class "numeric" ~~
siorder:Object of class "numeric" ~~
pcmodel:Object of class "PeriodicArmaModel" ~~
Class "SiPeriodicArmaModel", directly.
Class "VirtualPeriodicFilterModel", by class "SiPeriodicArmaModel", distance 2.
Class "PeriodicIntegratedArmaSpec", by class "SiPeriodicArmaModel", distance 2.
No methods defined with class "SiPeriodicMaModel" in the signature.
Functions for some basic operations with seasons.
toSeason(t, period, t1 = 1, from = 1) toSeasonPair(t, s, period, ...) ttTosl(r, period) ttmatToslPairs(i, j, period)toSeason(t, period, t1 = 1, from = 1) toSeasonPair(t, s, period, ...) ttTosl(r, period) ttmatToslPairs(i, j, period)
r |
covariance matrix, see ‘Details’. |
t |
a vector of integers, representing times. |
s |
a vector of integers, representing times. |
period |
the number of seasons. |
t1 |
time corresponding to the first season, an integer number. |
from |
1 or 0, depending on whether the season numbers start from 1 or 0. |
i |
a vector of integers. |
j |
a vector of integers. |
... |
todo: describe! |
ttmatToslPairs(i,j,period) transforms time-time pairs to
season-lag pairs. The time pairs are obtained by pairing each element
of i with each element of j. A four column matrix is
created with one row for each pair (t,s), such that
t=i[m] and s=j[n] for some m and n. The
row is m, n, s, l, where (s,l) is the season-lag pair
corresponding to (t,s).
ttTosl(r,period) converts autocovariances given in a covariance
matrix (i.e. in “tt” form) to the “sl” form. The result is a
period x (maxlag+1) matrix, where maxlag is the maximal
lag available in r. Entries for which no values are available
are filled with NA's. Warning is given if contradictory entries
are found (i.e. if r is not from a periodically correlated
process with the given period).
toSeason(t,period,t1=1,from=1) returns the season corresponding
to t. t1 is a time (integer) whose season is the first
season, from is 1 if the numbering of seasons is 1,2,...,period,
or 0 if the numbering of seasons is 0,1,...,period-1. Other values for
from are not admissible (but not checked). Note: some
of the functions in this package implicitly assume that t1=1 and
from=1.
toSeasonPair(t,s,period) converts the “tt” pair t,s to
“sl” pair and returns the result in the form of a list with elements
season and lag. Currently t and s must be
scalars.
pc.omitneg helps to implement dropping of negative indices in
season-lag objects. It returns its first argument, lags, if all
of its elements are non-negative. Otherwise, all elements of
lags must be non-positive. In this case the function creates the
vector 0:maxlag and drops the elements specified by lags. Note
that the default indexing will not work properly since zero elements in
an index are omitted (and there are such indices in season-lag
objects).
for ttmatToslPairs, a matrix with four columns;
for ttTosl, a matrix with period rows;
for toSeason(t,period,t1=1,from=1), a vector of integers;
for toSeasonPair(t,s,period), a list with elements
season and lag;
for pc.omitneg, a vector of lags (non-negative integers).
2013-10-24 - Corrected the description of the return value of
ttmatToslPairs. It incorrectly stated that the first two
columns are "tt" pair (they are actually indices in i and
j).
Georgi N. Boshnakov
Boshnakov GN, Iqelan BM (2009). “Generation of time series models with given spectral properties.” J. Time Series Anal., 30(3), 349–368. ISSN 0143-9782, doi:10.1111/j.1467-9892.2009.00617.x.
# ttmatToslPairs ttmatToslPairs(3, 3, 4) # 1, 1, 3, 0 ttmatToslPairs(3, 2, 4) # 1, 1, 3, 1 ttmatToslPairs(1:4, 1:4, 4) ttmatToslPairs(3:4, 3:4, 4) # ttTosl - :todo: # toSeason toSeason(1:10, 4) # 1 2 3 4 1 2 3 4 1 2 toSeason(1:10, 4, from = 0) # 0 1 2 3 0 1 2 3 0 1 ## first data is for 3rd quarter toSeason(1:10, 4, t1 = 3) # 3 4 1 2 3 4 1 2 3 4 # toSeasonPair toSeasonPair(3, 3, period=4) # season=3, lag = 0 toSeasonPair(8, 8, period=4) # season=4, lag = 0 toSeasonPair(3, 2, period=4) # season=3, lag = 1 toSeasonPair(7, 6, period=4) # same #### # pc.omitneg #### pc.omitneg(0:5,10) # 0:5, unchaged since all values >= 0 #### #### pc.omitneg(-(0:5),10) # 6:10, works like #### (0:10)[-(0:5 +1)] # same #### #### # don't mix positive and negative numbers in pc.omitneg #### \dontrun{pc.omitneg(c(0,2,3,-4,5), 10)}# ttmatToslPairs ttmatToslPairs(3, 3, 4) # 1, 1, 3, 0 ttmatToslPairs(3, 2, 4) # 1, 1, 3, 1 ttmatToslPairs(1:4, 1:4, 4) ttmatToslPairs(3:4, 3:4, 4) # ttTosl - :todo: # toSeason toSeason(1:10, 4) # 1 2 3 4 1 2 3 4 1 2 toSeason(1:10, 4, from = 0) # 0 1 2 3 0 1 2 3 0 1 ## first data is for 3rd quarter toSeason(1:10, 4, t1 = 3) # 3 4 1 2 3 4 1 2 3 4 # toSeasonPair toSeasonPair(3, 3, period=4) # season=3, lag = 0 toSeasonPair(8, 8, period=4) # season=4, lag = 0 toSeasonPair(3, 2, period=4) # season=3, lag = 1 toSeasonPair(7, 6, period=4) # same #### # pc.omitneg #### pc.omitneg(0:5,10) # 0:5, unchaged since all values >= 0 #### #### pc.omitneg(-(0:5),10) # 6:10, works like #### (0:10)[-(0:5 +1)] # same #### #### # don't mix positive and negative numbers in pc.omitneg #### \dontrun{pc.omitneg(c(0,2,3,-4,5), 10)}
Class "SubsetPM" - subset PAR models with trigonometric
parameterisation.
Objects can be created by calls of the form new("SubsetPM", ...)
but they are typically created by model fitting functions, see the examples.
theTS:"ANY", the time series to which the model is fitted.
period:"integer", the period.
order:"integer", the order.
findex:"function".
harmonics:"integer", Fourier harmonics to include in the model.
call:"call", the call used to fit the model.
other:"namedList".
signature(object = "SubsetPM"): ...
signature(object = "SubsetPM"): ...
signature(object = "SubsetPM"): ...
signature(object = "SubsetPM"): ...
signature(object = "SubsetPM"): ...
pcfr4 <- pcts(dataFranses1996)[[4]] x4 <- as.numeric(window(pcfr4, start = availStart(pcfr4), end = availEnd(pcfr4))) ## without 'harmonics' these models are equivalent tmpfit <- fit_trigPAR_optim(x4, 2, 4, tol = 1e-14, verbose = FALSE) tmpfitL <- fit_trigPAR_optim(x4, 2, 4, tol = 1e-14, type = "bylag", verbose = FALSE) ## for comparison tmpfitP <- pclsdf(x4, 4, 1:2, sintercept = FALSE) ## with intercept tmpfitc <- fit_trigPAR_optim(x4, 2, 4, tol = 1e-14, verbose = FALSE, sintercept = TRUE) tmpfitcn <- fit_trigPAR_optim(x4, 2, 4, tol = 1e-14, verbose = FALSE, sintercept = structure(TRUE, merge = TRUE)) tmpfitLc <- fit_trigPAR_optim(x4, 2, 4, tol = 1e-14, type = "bylag", verbose = FALSE, sintercept = TRUE) coef(tmpfitc, matrix = TRUE) coef(tmpfitcn, matrix = TRUE) coef(tmpfitLc, matrix = TRUE) coef(tmpfitc) coef(tmpfitcn) coef(tmpfitLc) coef(tmpfit) coef(tmpfitL) ## convert to PAR coefficients: coef(tmpfitc, type = "PAR", matrix = TRUE) coef(tmpfitcn, type = "PAR", matrix = TRUE) coef(tmpfitLc, type = "PAR", matrix = TRUE) coef(tmpfitL, type = "PAR", matrix = TRUE) predict(tmpfitc, n.ahead = 4) predict(tmpfitcn, n.ahead = 4) sqrt(diag((vcov(tmpfitL)))) e <- residuals(tmpfitL) fi <- fitted(tmpfitL)pcfr4 <- pcts(dataFranses1996)[[4]] x4 <- as.numeric(window(pcfr4, start = availStart(pcfr4), end = availEnd(pcfr4))) ## without 'harmonics' these models are equivalent tmpfit <- fit_trigPAR_optim(x4, 2, 4, tol = 1e-14, verbose = FALSE) tmpfitL <- fit_trigPAR_optim(x4, 2, 4, tol = 1e-14, type = "bylag", verbose = FALSE) ## for comparison tmpfitP <- pclsdf(x4, 4, 1:2, sintercept = FALSE) ## with intercept tmpfitc <- fit_trigPAR_optim(x4, 2, 4, tol = 1e-14, verbose = FALSE, sintercept = TRUE) tmpfitcn <- fit_trigPAR_optim(x4, 2, 4, tol = 1e-14, verbose = FALSE, sintercept = structure(TRUE, merge = TRUE)) tmpfitLc <- fit_trigPAR_optim(x4, 2, 4, tol = 1e-14, type = "bylag", verbose = FALSE, sintercept = TRUE) coef(tmpfitc, matrix = TRUE) coef(tmpfitcn, matrix = TRUE) coef(tmpfitLc, matrix = TRUE) coef(tmpfitc) coef(tmpfitcn) coef(tmpfitLc) coef(tmpfit) coef(tmpfitL) ## convert to PAR coefficients: coef(tmpfitc, type = "PAR", matrix = TRUE) coef(tmpfitcn, type = "PAR", matrix = TRUE) coef(tmpfitLc, type = "PAR", matrix = TRUE) coef(tmpfitL, type = "PAR", matrix = TRUE) predict(tmpfitc, n.ahead = 4) predict(tmpfitcn, n.ahead = 4) sqrt(diag((vcov(tmpfitL)))) e <- residuals(tmpfitL) fi <- fitted(tmpfitL)
Test if a time series is periodically integrated.
test_piar(x, d, p, sintercept = FALSE, sslope = FALSE, homoschedastic = FALSE)test_piar(x, d, p, sintercept = FALSE, sslope = FALSE, homoschedastic = FALSE)
x |
time series. |
d |
period. |
p |
autoregressive order, a positive integer. |
sintercept |
if TRUE, include seasonal intercept. |
sslope |
if TRUE, include seasonal slope. |
homoschedastic |
if TRUE, assume the innovations variance is the same for all seasons. |
Computes test statistics for Franses (1996) test for periodic
integration of order 1. The test is based on periodic autoregression
of order p, where p can be any positive integer.
a list with the following components:
p |
autoregressive order. |
spec |
values of |
statistics |
a matrix containing the test statistics (first row) and the
corresponding p-values (second row). |
Currently only the case p = 1 is handled, for p > 1 the
statistics are set to NA. :TODO: handle this.
All statistics are computed but some p-values are not computed yet.
Georgi N. Boshnakov
Boswijk HP and Franses PH (1996). “Unit roots in periodic autoregressions.” Journal of Time Series Analysis, 17(3), pp. 221–245.
ts1 <- window(dataFranses1996[ , "CanadaUnemployment"], start = c(1960, 1), end = c(1987, 4)) test_piar(ts1, 4, 1, sintercept = TRUE) pcTest(ts1, "piar", 4, 1, sintercept = TRUE) # same test_piar(ts1, 4, 1, sintercept = TRUE, sslope = TRUE) test_piar(ts1, 4, 1) test_piar(ts1, 4, 1, homoschedastic = TRUE)ts1 <- window(dataFranses1996[ , "CanadaUnemployment"], start = c(1960, 1), end = c(1987, 4)) test_piar(ts1, 4, 1, sintercept = TRUE) pcTest(ts1, "piar", 4, 1, sintercept = TRUE) # same test_piar(ts1, 4, 1, sintercept = TRUE, sslope = TRUE) test_piar(ts1, 4, 1) test_piar(ts1, 4, 1, homoschedastic = TRUE)
unitCycle and unitSeason in package pctsMethods for unitCycle and unitSeason in package pcts.
unitCycle and unitSeason have methods with identical
signatures:
signature(x = "ANY")signature(x = "VirtualPeriodicModel")signature(x = "Cyclic")signature(x = "SimpleCycle")signature(x = "PartialCycle")signature(x = "OpenCloseCycle")signature(x = "QuarterYearCycle")signature(x = "DayWeekCycle")signature(x = "MonthYearCycle")signature(x = "Every30MinutesCycle")allSeasons for examples and related functions
## presidents is a quarterly time series in base-R tsp(presidents) pc_presidents <- pcts(presidents) unitCycle(pc_presidents) unitSeason(pc_presidents)## presidents is a quarterly time series in base-R tsp(presidents) pc_presidents <- pcts(presidents) unitCycle(pc_presidents) unitSeason(pc_presidents)
`unitCycle<-` and `unitSeason<-` in package pctsMethods for `unitCycle<-` and `unitSeason<-`
in package pcts.
`unitCycle<-` and `unitSeason<-` have methods with identical
signatures:
signature(x = "Cyclic")signature(x = "SimpleCycle")allSeasons for related functions and examples
qrt <- BuiltinCycle(4) unitSeason(qrt) # "Quarter" unitCycle(qrt) # "Year" moreve <- new("SimpleCycle", 2) unitSeason(moreve) # "Season" unitCycle(moreve) # "Cycle" allSeasons(moreve) # c("Season_1", "Season_2") ## change the names unitCycle(moreve) <- "Day" unitSeason(moreve) <- "TimeOfDay" allSeasons(moreve) <- c("Morning", "Evening") unitSeason(moreve) unitCycle(moreve) allSeasons(moreve)qrt <- BuiltinCycle(4) unitSeason(qrt) # "Quarter" unitCycle(qrt) # "Year" moreve <- new("SimpleCycle", 2) unitSeason(moreve) # "Season" unitCycle(moreve) # "Cycle" allSeasons(moreve) # c("Season_1", "Season_2") ## change the names unitCycle(moreve) <- "Day" unitSeason(moreve) <- "TimeOfDay" allSeasons(moreve) <- c("Morning", "Evening") unitSeason(moreve) unitCycle(moreve) allSeasons(moreve)
Extract the core data from a periodic time series as a vector, matrix or array.
Vec(x, ...) tsMatrix(x, ...) tsVector(x, ...) tsVec(x, ...) pcMatrix(x, ...) pcArray(x, ndim = 3, ...) pctsArray(x, ndim = 3, ...)Vec(x, ...) tsMatrix(x, ...) tsVector(x, ...) tsVec(x, ...) pcMatrix(x, ...) pcArray(x, ndim = 3, ...) pctsArray(x, ndim = 3, ...)
x |
an object. |
... |
further arguments for methods. |
ndim |
currently not used. |
These functions give the core data in various common forms.
The data values can be extracted as a vector from a periodic time
series object, say x, with as.vector(x) or as(x,
"vector"). For multivariate time series the vector returned by
as.vector(x) (or as(x, "vector")) is equivalent to
as.vector(as.matrix(x)).
Similarly, as.matrix() and as(x, "matrix")
extract the data as a matrix containing one column per variable.
Vec() is like as.vector() but the result is a matrix
with one column (column vector). The default does literally this.
Thus both, Vec() and as.vector(), implement the
Vec operation from matrix calculus but the latter returns the
result as a vector, not matrix.
The most common representation of data in statistics is matrix-like with one column per variable. The descriptions of algorithms for multivariate time series however usually define the vector of observations at a given time to be a column vector. In particular, implementations of the Kalman filter often require precisely this arrangement. In that case the data matrix is the transposed of the more common one and the vectorising operation stacks the observations, not the variables.
The functions tsMatrix(), tsVector() and tsVec()
provide the analogues of as.vector(), as.matrix() and
Vec() for the “transposed” arrangement.
These functions may look redundant since they are simple combinations of the above and traspose operations. Having functions makes for more readable programming. They may be more efficient, as well, for example if the underlying time series class stores the data in the transposed format.
pcMatrix() and pcArray() also give the core
data. Effectively, they give an additional dimension to the
seasons. The season becomes the first dimension since for column
oriented data the season changes fastest. pcMatrix is most
suitable for univariate time series, pcArray() for
multivariate. Note that pcArray() easily extends to multiple
periodicities although currently (2019-04-19) there are no methods
that exploit this.
For univariate time series, in the matrix returned by
pcMatrix() each row represents the data for one season and each
column for one cycle. For multivariate time series, the matrices for
each variable are put next to each other.
pcArray() returns the data as an array, whose last dimension
corresponds to variables. In the default case the array is
3-dimensonal with dimensions (season, year, variable).
pctsArray() is a variant of pcArray() corresponding to
the arrangement of tsMatrix(). The ordering of the dimensions
here is (variable, season, cycle).
vector, matrix or array, as indicated by the name of the function and described in section ‘Details’.
Georgi N. Boshnakov
## window to make number of years different from number of months ap <- pcts(window(AirPassengers, start = c(1956, 1))) class( as.vector(ap) ) class( as(ap, "vector") ) dim( as.matrix(ap) ) dim( as(ap, "matrix") ) dim( tsMatrix(ap) ) class( tsVector(ap) ) dim( tsVec(ap) ) dim( pcMatrix(ap) ) dim( pcArray(ap) ) dim( pctsArray(ap) ) dfr <- pcts(dataFranses1996) dim(dfr) # c(148, 19) nSeasons(dfr) # 4 length(as.vector(dfr)) all.equal(as.vector(dfr)[1:148], as.matrix(dfr)[ , 1]) # TRUE all.equal(tsVector(dfr)[1:19], unname(as.matrix(dfr)[1, ])) # TRUE dim( as.matrix(dfr) ) # c(148, 19) dim( tsMatrix(dfr) ) # c(19, 148) all.equal(tsMatrix(dfr)[ , 1], as.matrix(dfr)[1, ]) # TRUE dim( Vec(dfr) ) dim( tsVec(dfr) ) all.equal(tsVec(dfr)[1:19], unname(as.matrix(dfr)[1, ])) # TRUE dim( pcMatrix(dfr) ) # c(4, 703), one row for each season dim( pcArray(dfr) ) # c(4, 37, 19), note: 703 == 37*19 dim( pctsArray(dfr) ) # c(19, 4, 37), note: 703 == 37*19## window to make number of years different from number of months ap <- pcts(window(AirPassengers, start = c(1956, 1))) class( as.vector(ap) ) class( as(ap, "vector") ) dim( as.matrix(ap) ) dim( as(ap, "matrix") ) dim( tsMatrix(ap) ) class( tsVector(ap) ) dim( tsVec(ap) ) dim( pcMatrix(ap) ) dim( pcArray(ap) ) dim( pctsArray(ap) ) dfr <- pcts(dataFranses1996) dim(dfr) # c(148, 19) nSeasons(dfr) # 4 length(as.vector(dfr)) all.equal(as.vector(dfr)[1:148], as.matrix(dfr)[ , 1]) # TRUE all.equal(tsVector(dfr)[1:19], unname(as.matrix(dfr)[1, ])) # TRUE dim( as.matrix(dfr) ) # c(148, 19) dim( tsMatrix(dfr) ) # c(19, 148) all.equal(tsMatrix(dfr)[ , 1], as.matrix(dfr)[1, ]) # TRUE dim( Vec(dfr) ) dim( tsVec(dfr) ) all.equal(tsVec(dfr)[1:19], unname(as.matrix(dfr)[1, ])) # TRUE dim( pcMatrix(dfr) ) # c(4, 703), one row for each season dim( pcArray(dfr) ) # c(4, 37, 19), note: 703 == 37*19 dim( pctsArray(dfr) ) # c(19, 4, 37), note: 703 == 37*19
Periodic methods for base R functions.
## S3 method for class 'PeriodicTS' window(x, start = NULL, end = NULL, seasons = NULL, ...) ## S3 method for class 'PeriodicMTS' window(x, start = NULL, end = NULL, seasons = NULL, ...) ## S3 method for class 'PeriodicTS' na.trim(object, sides = c("both", "left", "right"), ...) ## S3 method for class 'PeriodicMTS' na.trim(object, sides = c("both", "left", "right"), is.na = c("any", "all"), ...) ## S3 method for class 'PeriodicTimeSeries' frequency(x, ...) ## S3 method for class 'PeriodicTimeSeries' deltat(x, ...) ## S3 method for class 'PeriodicTimeSeries' cycle(x, ...) ## S3 method for class 'PeriodicTimeSeries' time(x, offset = 0, ...) ## S3 method for class 'Cyclic' start(x, ...) ## S3 method for class 'Cyclic' end(x, ...)## S3 method for class 'PeriodicTS' window(x, start = NULL, end = NULL, seasons = NULL, ...) ## S3 method for class 'PeriodicMTS' window(x, start = NULL, end = NULL, seasons = NULL, ...) ## S3 method for class 'PeriodicTS' na.trim(object, sides = c("both", "left", "right"), ...) ## S3 method for class 'PeriodicMTS' na.trim(object, sides = c("both", "left", "right"), is.na = c("any", "all"), ...) ## S3 method for class 'PeriodicTimeSeries' frequency(x, ...) ## S3 method for class 'PeriodicTimeSeries' deltat(x, ...) ## S3 method for class 'PeriodicTimeSeries' cycle(x, ...) ## S3 method for class 'PeriodicTimeSeries' time(x, offset = 0, ...) ## S3 method for class 'Cyclic' start(x, ...) ## S3 method for class 'Cyclic' end(x, ...)
x, object
|
an object from the indicated periodic class. |
start |
|
end |
|
seasons |
numeric, a subset of |
... |
Not used by these methods. |
sides |
which side to trim: start ( |
is.na |
for multivariate time series: if |
offset |
currently ignored (:TODO:) |
Periodic methods for base R and other common functions for manipulation of time series. These methods work analogoulsly to their base R cousins and only the differences, if any, are discussed below.
window takes a part of x, preserving the
class of the object. Argument seasons selects a subset of the
seasons.
na.trim is a function defined in package zoo
and re-exported by pcts. It trims NAs from one or both
ends of the time series, as requested by the arguments. The arguments
of the methods defined by pcts have the same meaning as those in
zoo.
for window and na.trim,
an object from the same class as the original, representing the
requested part of the time series.
for frequency, an integer number.
for deltat, a number (1/frequency).
for cycle and time, a "PeriodicTS" object.
for start and end, time of first/last observation,
encoded as a pair of numbers.
window,
frequency,
na.trim for details on what these functions do.
availStart and availEnd give the times of
the first and last non-NA observations.
pres <- pcts(presidents) head(pres, 8) availStart(pres) tail(pres, 12) availEnd(pres) ## Q3 and Q4 only presQ3Q4 <- window(pres, seasons = 3:4) head(presQ3Q4) identical(na.trim(pres), window(pres, start = availStart(pres), end = availEnd(pres))) ## TRUEpres <- pcts(presidents) head(pres, 8) availStart(pres) tail(pres, 12) availEnd(pres) ## Q3 and Q4 only presQ3Q4 <- window(pres, seasons = 3:4) head(presQ3Q4) identical(na.trim(pres), window(pres, start = availStart(pres), end = availEnd(pres))) ## TRUE
Class zoo made S4
A virtual Class: No objects may be created from it.
S4 Class "zoo" is derived from its namesake in package
zoo for use as a super class for periodic time series classes
and in S4 method signatures.
.S3Class:Object of class "character" ~~
Class "oldClass", directly.
No methods defined with class "zoo" in the signature.
PeriodicTS_zooreg,
zooreg
and package zoo
showClass("zoo")showClass("zoo")
Virtual S4 class zooreg.
A virtual Class: No objects may be created from it.
S4 Class "zooreg" is derived from its namesake in package
zoo for use as a super class for periodic time series classes
and in S4 method signatures.
.S3Class:Object of class "character" ~~
Class "zoo", directly.
Class "oldClass", by class "zoo", distance 2.
No methods defined with class "zooreg" in the signature.
PeriodicTS_zooreg,
zoo
and package zoo
showClass("zooreg")showClass("zooreg")