perARMA (version 1.4)

perYW: Yule-Walker estimators of PAR model

Description

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.

Usage

perYW(x, T, p, missval)

Arguments

x

input time series.

T

period of PC-T structure (assumed constant over time).

p

order of the autoregression.

missval

notation for missing values.

Value

• estimated parameters of PAR(p) model:
• phi
  matrix of coefficients for autoregressive part.
• del
  vector of noise weights (consider them variances of the shocks).

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.

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.

See Also

predictperYW, loglikef, parmaf

Examples

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