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.
1 2  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 
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. 
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 = μ_s + α_s y_{t1} + β_s (y_{t1}  α_{s1} y_{t2}) + ε_t,
for s=1,...,S, two different hypotheses can be tested:
H0: α_s = 1, for s=1,...S1,
H0: α_s = 1, for s=1,...S1.
For S=4, if the hypothesis α_1*α_2*α_3*α_4=1 cannot be rejected (see LRurpar.test), the null hypotheses above entails that either α_4=1 or α_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, (1L), 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 Fstatistic is F(S1, nk), 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.partsmclass
containing the Ftest statistic, the freedom
degrees an the corresponding pvalue.
Javier LopezdeLacalle javlacalle@yahoo.es.
Ftest.partsmclass
, and LRurpar.test
.
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