partsm (version 1.1-4)

Fpar.test: Test for Periodic Variation in the Autoregressive Parameters

Description

Test for periodic variation in the autoregressive parameters.

Usage

Fpar.test (wts, detcomp, p)

Value

An object of class Ftest.partsm-class containing the \(F\)-test statistic, the freedom degrees an the corresponding \(p\)-value.

Arguments

wts

a univariate time series object.

detcomp

a vector indicating the deterministic components included in the auxiliary regression. See the corresponding item in fit.ar.par.

p

the order of the initial AR or PAR model.

Author

Javier Lopez-de-Lacalle .

Details

An F-test based on the residual sum of squares is performed to test for periodic variation in the autoregressive parameters.

On the basis of the following model,

$$y_t = \phi_{1s} y_{t-1} + ... + \phi_{ps} y_{t-p} + \epsilon_t,$$

for \(s=1,...,S\), where S is the periodicity of the time series,

the null-hypothesis is non-periodicity: \(\phi_{is}=\phi_i\), for \(s=1,...,S\) and \(i=1,2,...,p\). When the null hypothesis is imposed an AR(p) is estimated, whereas the alternative is a PAR(p) model.

The F-statistic when four seasonal intercepts are included follows an F((S-1)*p, n-(S+S*p)) distribution, where S is the periodicity of the series and n the number of observations.

See Also

fit.ar.par, and Ftest.partsm-class.

Examples

    ## Test for periodicity in a second order PAR model for
    ## the logarithms of the Real GNP in Germany time series.
    data("gergnp")
    lgergnp <- log(gergnp, base=exp(1))
    detcomp <- list(regular=c(0,0,0), seasonal=c(1,0), regvar=0)
    out <- Fpar.test(wts=lgergnp, detcomp=detcomp, p=2)