| predictpiar {partsm} | R Documentation |
Predictions for a Restricted Periodic Autoregressive Model
Description
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 observed data.
Usage
predictpiar (wts, p, hpred)
Arguments
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. |
Details
Upon the multivariate representation,
\Phi_0 y_t = \Psi + \Phi_1 Y_{T-1} + ... + \Phi_P y_{T-P} + \epsilon_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} + \epsilon_T .
Multi-step-ahead forecasts are obtained recursively.
The prediction errors variances for the one-step-ahead forecast are the diagonal elements of
\sigma^2 \Phi_0^{-1} (\Phi_0^{-1})^{'},
whereas for h=2,3,... years ahead forecasts it becomes
\sigma^2 \Phi_0^{-1} (\Phi_0^{-1})^{'} + (h-1) (\Gamma \Phi_0^{-1}) (\Gamma \Phi_0^{-1})^{'},
where \Gamma = \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.
Value
An object of class pred.piartsm-class containing the forecasts and the corresponding
standard errors, as well as the 95 per cent confidence intervals.
Author(s)
Javier Lopez-de-Lacalle javlacalle@yahoo.es.
References
P.H. Franses: Periodicity and Stochastic Trends in Economic Time Series (Oxford University Press, 1996).
See Also
fit.piar, PAR.MVrepr-methods, and pred.piartsm-class.
Examples
## 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)