This function performs predictions for a restricted periodic autoregressive model. This version considers PIAR models up to order 2 with seasonal intercepts. It is implemented for quarterly oberved data.
1 2  predictpiar (wts, p, hpred)

wts 
a univariate time series object. 
p 
the order of the PAR model. At present first and second order are considered. 
hpred 
number of outofsample observations to forecast. It must be a multiple of 4. 
Upon the multivariate representation,
Φ_0 y_t = Ψ + Φ_1 Y_{T1} + ... + Φ_P y_{TP} + ε_T ,
where the Φ_i, i=1,2,...,P are s \times s matrices containing the φ_{is} parameters., the onestepahead forecasts for the year T+1 is straightforward,
y_t = Φ_0^{1} Ψ + Φ_0^{1} Φ_1 Y_{T1} + ... + Φ_0^{1} Φ_P y_{TP} + Φ_0^{1} + ε_T .
Multistepahead forecasts are obtained recursively.
The prediction errors variances for the onestepahead forecast are the diagonal elements of
σ^2 Φ_0^{1} (Φ_0^{1})^{'},
whereas for h=2,3,... years ahead forecasts it becomes
σ^2 Φ_0^{1} (Φ_0^{1})^{'} + (h1) (Γ Φ_0^{1}) (Γ Φ_0^{1})^{'},
where Γ = Φ_0^{1} Φ_1.
This version considers PIAR models up to order 2 for quarterly observed data. By default, seasonal intercepts are included in the model as deterministic components.
The number of observations to forecast, hpred
must be a multiple of 4.
An object of class pred.piartsmclass
containing the forecasts and the corresponding
standard errors, as well as the 95 per cent confidence intervals.
Javier LopezdeLacalle javlacalle@yahoo.es.
P.H. Franses: Periodicity and Stochastic Trends in Economic Time Series (Oxford University Press, 1996).
fit.piar
, PAR.MVreprmethods
, and pred.piartsmclass
.
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Questions? Problems? Suggestions? Tweet to @rdrrHQ or email at ian@mutexlabs.com.
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