Description Usage Arguments Details Value Author(s) References See Also Examples

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.

1 | ```
perYW(x, T, p, missval)
``` |

`x` |
input time series. |

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

`p` |
order of the autoregression. |

`missval` |
notation for missing values. |

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.

estimated parameters of PAR(p) model:

`phi` |
matrix of coefficients for autoregressive part. |

`del` |
vector of noise weights (consider them variances of the shocks). |

Harry Hurd

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`

1 2 |

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