Fpari.piar.test {partsm} | R Documentation |
This function performs a test for a parameter restriction in a PAR model. Two restrictions can be considered and entail that the process contain either the unit root 1 or the seasonal unit root -1. In this version PAR models up to order 2 can be considered.
Fpari.piar.test (wts, detcomp, p, type)
wts |
a univariate time series object. |
detcomp |
a vector indicating the deterministic components included in the auxiliar regression. See
the corresponding item in fit.ar.par . |
p |
the order of the initial AR or PAR model. In this version PAR models up to order 2 with seasonal intercepts are considered. |
type |
a character string indicating which restriction should be tested. "PARI1" inidicates
that the unit root is tested whereas "PARI-1" test for the unit root -1. |
On the basis of the following PAR model (in this version PAR models up to order 2 are considered and seasonal intercepts are included default),
y_t = \mu_s + \alpha_s y_{t-1} + \beta_s (y_{t-1} - \alpha_{s-1} y_{t-2}) + \epsilon_t,
for s=1,...,S, two different hypotheses can be tested:
For S=4, if the hypothesis \alpha_1*\alpha_2*\alpha_3*\alpha_4=1 cannot be rejected (see LRurpar.test), the null hypotheses above entails that either \alpha_4=1 or \alpha_4=-1.
When the first H0 is not rejected, the PAR model contains the unit root 1, and the periodic difference filter is just the first order difference, (1-L), where L is the lag operator.
When the second H0 is not rejected, the PAR model contains the unit root -1, and the periodic difference filter is simplified as (1+L).
In both null hypotheses it is said that the data behave as a PAR model for an integrated series, known as PARI. If those null hypotheses are rejected, the corresponding model is called a periodically integrated autoregressive model, PIAR.
The asymptotic distribution of the F-statistic is F(S-1, n-k), where n is the number of observations and k the number of regressors.
In this version PAR models up to order 2 can be considered.
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.
Ftest.partsm-class
, and LRurpar.test
.
## Test for the unit root 1 in a PAR(2) with seasonal intercepts for ## the logarithms of the Real GNP in Germany. data("gergnp") lgergnp <- log(gergnp, base=exp(1)) detcomp <- list(regular=c(0,0,0), seasonal=c(1,0), regvar=0) out <- Fpari.piar.test(wts=lgergnp, detcomp=detcomp, p=2, type="PARI1")