Fit PAR models using least squares
pclsdf.RdFit PAR models using least squares. The model may contain intercepts and linear trends, seasonal or non-seasonal.
Usage
pclsdf(x, d, lags = integer(0), sintercept = TRUE, sslope = FALSE,
intercept = FALSE, slope = FALSE, xreg, contrasts = NULL,
seasonof1st = NULL, coefonly = FALSE)Arguments
- x
time series, a numeric vector.
- d
period, an integer.
- lags
an integer vector, typically
1:p, wherepis the order of the autoregression. The same lags are used for all seasons.- 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
lm.
Details
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.
Value
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
lm, a character string.- fit
(if
coefonly = FALSE) the fitted object obtained fromlm.
Note
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.
Examples
## data(dataFranses1996)
cu <- pcts(dataFranses1996[ , "CanadaUnemployment"])
cu <- window(cu, start = availStart(cu), end = availEnd(cu))
pclsdf(cu, 4, 1:2, sintercept = TRUE)
#> $par
#> [,1] [,2]
#> [1,] 1.6727479 -0.6086116
#> [2,] 0.6076993 0.4000458
#> [3,] 1.6703750 -0.7011981
#> [4,] 1.1580936 -0.2012461
#>
#> $sintercept
#> Season1 Season2 Season3 Season4
#> 103.87879 -27.91949 27.53365 47.18863
#>
#> $sigma2hat
#> [1] 1917.9150 3967.1090 899.7107 1314.2189
#>
#> $formula.char
#> [1] "x ~ -1 + Season + Lagged_1:Season + Lagged_2:Season"
#>
#> $fit
#>
#> Call:
#> lm(formula = fomodel, data = res, na.action = na.exclude)
#>
#> Coefficients:
#> Season1 Season2 Season3 Season4
#> 103.8788 -27.9195 27.5336 47.1886
#> Season1:Lagged_1 Season2:Lagged_1 Season3:Lagged_1 Season4:Lagged_1
#> 1.6727 0.6077 1.6704 1.1581
#> Season1:Lagged_2 Season2:Lagged_2 Season3:Lagged_2 Season4:Lagged_2
#> -0.6086 0.4000 -0.7012 -0.2012
#>
#>
pclsdf(austres, 4, lags = 1:3)
#> $par
#> [,1] [,2] [,3]
#> [1,] 1.528572 -0.26968659 -0.25942556
#> [2,] 1.335708 0.06294708 -0.39888301
#> [3,] 1.257598 0.34822562 -0.60613046
#> [4,] 1.650766 -0.63662585 -0.01077079
#>
#> $sintercept
#> Season1 Season2 Season3 Season4
#> 11.08871 14.87099 18.57018 -32.42783
#>
#> $sigma2hat
#> [1] 36.39442 105.19204 33.77605 96.32893
#>
#> $formula.char
#> [1] "x ~ -1 + Season + Lagged_1:Season + Lagged_2:Season + Lagged_3:Season"
#>
#> $fit
#>
#> Call:
#> lm(formula = fomodel, data = res, na.action = na.exclude)
#>
#> Coefficients:
#> Season1 Season2 Season3 Season4
#> 11.08871 14.87099 18.57018 -32.42783
#> Season1:Lagged_1 Season2:Lagged_1 Season3:Lagged_1 Season4:Lagged_1
#> 1.52857 1.33571 1.25760 1.65077
#> Season1:Lagged_2 Season2:Lagged_2 Season3:Lagged_2 Season4:Lagged_2
#> -0.26969 0.06295 0.34823 -0.63663
#> Season1:Lagged_3 Season2:Lagged_3 Season3:Lagged_3 Season4:Lagged_3
#> -0.25943 -0.39888 -0.60613 -0.01077
#>
#>
pclsdf(austres, 4, lags = 1:3, sintercept = TRUE)
#> $par
#> [,1] [,2] [,3]
#> [1,] 1.528572 -0.26968659 -0.25942556
#> [2,] 1.335708 0.06294708 -0.39888301
#> [3,] 1.257598 0.34822562 -0.60613046
#> [4,] 1.650766 -0.63662585 -0.01077079
#>
#> $sintercept
#> Season1 Season2 Season3 Season4
#> 11.08871 14.87099 18.57018 -32.42783
#>
#> $sigma2hat
#> [1] 36.39442 105.19204 33.77605 96.32893
#>
#> $formula.char
#> [1] "x ~ -1 + Season + Lagged_1:Season + Lagged_2:Season + Lagged_3:Season"
#>
#> $fit
#>
#> Call:
#> lm(formula = fomodel, data = res, na.action = na.exclude)
#>
#> Coefficients:
#> Season1 Season2 Season3 Season4
#> 11.08871 14.87099 18.57018 -32.42783
#> Season1:Lagged_1 Season2:Lagged_1 Season3:Lagged_1 Season4:Lagged_1
#> 1.52857 1.33571 1.25760 1.65077
#> Season1:Lagged_2 Season2:Lagged_2 Season3:Lagged_2 Season4:Lagged_2
#> -0.26969 0.06295 0.34823 -0.63663
#> Season1:Lagged_3 Season2:Lagged_3 Season3:Lagged_3 Season4:Lagged_3
#> -0.25943 -0.39888 -0.60613 -0.01077
#>
#>
pclsdf(austres, 4, lags = 1:3, sintercept = TRUE, sslope = TRUE)
#> $par
#> [,1] [,2] [,3]
#> [1,] 1.370470 0.05946978 -0.4607858
#> [2,] 1.282184 0.10653624 -0.4132554
#> [3,] 1.291900 0.31313365 -0.5901552
#> [4,] 1.859568 -1.01171474 0.1055395
#>
#> $sintercept
#> Season1 Season2 Season3 Season4
#> 395.6552 327.4550 -176.4203 601.7557
#>
#> $sslope
#> Season1:TimeIndex Season2:TimeIndex Season3:TimeIndex Season4:TimeIndex
#> 1.6136930 1.2845380 -0.8039129 2.6183438
#>
#> $sigma2hat
#> [1] 28.99261 98.63279 31.33658 71.72827
#>
#> $formula.char
#> [1] "x ~ -1 + Season + TimeIndex:Season + Lagged_1:Season + Lagged_2:Season + Lagged_3:Season"
#>
#> $fit
#>
#> Call:
#> lm(formula = fomodel, data = res, na.action = na.exclude)
#>
#> Coefficients:
#> Season1 Season2 Season3 Season4
#> 395.65518 327.45502 -176.42026 601.75566
#> Season1:TimeIndex Season2:TimeIndex Season3:TimeIndex Season4:TimeIndex
#> 1.61369 1.28454 -0.80391 2.61834
#> Season1:Lagged_1 Season2:Lagged_1 Season3:Lagged_1 Season4:Lagged_1
#> 1.37047 1.28218 1.29190 1.85957
#> Season1:Lagged_2 Season2:Lagged_2 Season3:Lagged_2 Season4:Lagged_2
#> 0.05947 0.10654 0.31313 -1.01171
#> Season1:Lagged_3 Season2:Lagged_3 Season3:Lagged_3 Season4:Lagged_3
#> -0.46079 -0.41326 -0.59016 0.10554
#>
#>
x <- rep(1:4,10)
pclsdf(x, 4, lags = 1:3, sintercept = TRUE, sslope = TRUE)
#> $par
#> [,1] [,2] [,3]
#> [1,] NA NA NA
#> [2,] NA NA NA
#> [3,] NA NA NA
#> [4,] NA NA NA
#>
#> $sintercept
#> Season1 Season2 Season3 Season4
#> 1 2 3 4
#>
#> $sslope
#> Season1:TimeIndex Season2:TimeIndex Season3:TimeIndex Season4:TimeIndex
#> 8.816396e-18 -1.469171e-18 2.383641e-17 5.209739e-17
#>
#> $sigma2hat
#> [1] 1.934585e-32 5.372172e-34 1.414124e-31 9.553764e-31
#>
#> $formula.char
#> [1] "x ~ -1 + Season + TimeIndex:Season + Lagged_1:Season + Lagged_2:Season + Lagged_3:Season"
#>
#> $fit
#>
#> Call:
#> lm(formula = fomodel, data = res, na.action = na.exclude)
#>
#> Coefficients:
#> Season1 Season2 Season3 Season4
#> 1.000e+00 2.000e+00 3.000e+00 4.000e+00
#> Season1:TimeIndex Season2:TimeIndex Season3:TimeIndex Season4:TimeIndex
#> 8.816e-18 -1.469e-18 2.384e-17 5.210e-17
#> Season1:Lagged_1 Season2:Lagged_1 Season3:Lagged_1 Season4:Lagged_1
#> NA NA NA NA
#> Season1:Lagged_2 Season2:Lagged_2 Season3:Lagged_2 Season4:Lagged_2
#> NA NA NA NA
#> Season1:Lagged_3 Season2:Lagged_3 Season3:Lagged_3 Season4:Lagged_3
#> NA NA NA NA
#>
#>
## 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" ))