Fpar.test: Test for Periodic Variation in the Autoregressive Parameters
In partsm: Periodic Autoregressive Time Series Models

Description Usage Arguments Details Value Author(s) See Also Examples

Test for periodic variation in the autoregressive parameters.

1 2	Fpar.test (wts, detcomp, p)

`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.

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 = φ_{1s} y_{t-1} + ... + φ_{ps} y_{t-p} + ε_t,

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

the null-hypothesis is non-periodicity: φ_{is}=φ_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.

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

Javier Lopez-de-Lacalle javlacalle@yahoo.es.

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

    ## 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)