Assuming known T, procedure perYW implements Yule-Walker
estimation method for a periodic autoregressive PAR(p) model.
Order of autoregression p, which could be specified using sample
periodic PACF, is constant
for all seasons. For input time series x, matrix of parameters
phi and vector of parameters
del are computed.
perYW(x, T_t, p, missval)estimated parameters of PAR(p) model:
matrix of coefficients for autoregressive part.
vector of noise weights (consider them variances of the shocks).
input time series.
period of PC-T structure (assumed constant over time).
order of the autoregression.
notation for missing values.
Harry Hurd
For fixed T, this procedure implements a periodic version of the
Yule-Walker algorithm.
The algorithm is based on solving for the best coefficients of
LS prediction of \(X(t)\) in terms of \(X(t-1),...,X(t-p+1)\).
Sample autocorrelations are used in place
of population autocorrelations in the expressions of the best coefficients.
Brockwell, P. J., Davis, R. A. (1991), Time Series: Theory and Methods, 2nd Ed., Springer: New York.
Vecchia, A., (1985), Maximum Likelihood Estimation for Periodic Autoregressive Moving Average Models, Technometrics, v. 27, pp.375-384.
predictperYW, loglikef, parmaf
data(volumes)
perYW(volumes,24,2,NaN)
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