predictpiar {partsm} | R Documentation |
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.
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 out-of-sample observations to forecast. It must be a multiple of 4. |
Upon the multivariate representation,
Phi_0 y_t = Psi + Phi_1 Y_{T-1} + ... + Phi_P y_{T-P} + ε_T ,
where the Phi_i, i=1,2,...,P are s times s matrices containing the phi_{is} parameters., the one-step-ahead forecasts for the year T+1 is straightforward,
y_t = Phi_0^{-1} Psi + Phi_0^{-1} Phi_1 Y_{T-1} + ... + Phi_0^{-1} Phi_P y_{T-P} + Phi_0^{-1} + ε_T .
Multi-step-ahead forecasts are obtained recursively.
The prediction errors variances for the one-step-ahead forecast are the diagonal elements of
σ^2 Phi_0^{-1} (Phi_0^{-1})^{'},
whereas for h=2,3,... years ahead forecasts it becomes
σ^2 Phi_0^{-1} (Phi_0^{-1})^{'} + (h-1) (Γ Phi_0^{-1}) (Γ Phi_0^{-1})^{'},
where Γ = Phi_0^{-1} Phi_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.piartsm-class
containing the forecasts and the corresponding
standard errors, as well as the 95 per cent confidence intervals.
Javier López-de-Lacalle javlacalle@yahoo.es.
P.H. Franses: Periodicity and Stochastic Trends in Economic Time Series (Oxford University Press, 1996).
fit.piar
, PAR.MVrepr-methods
, and pred.piartsm-class
.
## 24 step-ahead forecasts in a PIAR(2) model for the ## logarithms of the Real GNP in Germany. data("gergnp") lgergnp <- log(gergnp, base=exp(1)) pred.out <- predictpiar(wts=lgergnp, p=2, hpred=24)