Fpari.piar.test {partsm} | R Documentation |
Test for a Parameter Restriction in a PAR Model.
Description
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.
Usage
Fpari.piar.test (wts, detcomp, p, type)
Arguments
wts |
a univariate time series object. |
detcomp |
a vector indicating the deterministic components included in the auxiliary regression. See
the corresponding item in |
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. |
Details
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:
-
H0: \alpha_s = 1, for s=1,...S-1
, -
H0: \alpha_s = -1, for s=1,...S-1
.
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.
Value
An object of class Ftest.partsm-class
containing the F
-test statistic, the freedom
degrees an the corresponding p
-value.
Author(s)
Javier Lopez-de-Lacalle javlacalle@yahoo.es.
See Also
Ftest.partsm-class
, and LRurpar.test
.
Examples
## 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")