perYW function

Yule-Walker estimators of PAR model

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)

Arguments

• x: input time series.
• T_t: period of PC-T structure (assumed constant over time).
• p: order of the autoregression.
• missval: notation for missing values.

Details

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.

Returns

estimated parameters of PAR(p) model: - phi: matrix of coefficients for autoregressive part.

• del: vector of noise weights (consider them variances of the shocks).

References

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.

Author(s)

Harry Hurd

See Also

predictperYW, loglikef, parmaf

Examples

data(volumes)
perYW(volumes,24,2,NaN)