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Maximum likelihood estimation for periodic autoregressive moving average models

Technometrics

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https://doi.org/10.1080/00401706.1985.10488076

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Abstract

A useful class of models for seasonal time series that cannot be filtered or standardized to achieve second-order stationarity is that of periodic autoregressive moving average (PARMA) models, which are extensions of ARMA models that allow periodic (seasonal) parameters. An approximation to the exact likelihood for Gaussian PARMA processes is developed, and a straightforward algorithm for its maximization is presented. The algorithm is tested on several periodic ARMA(1, 1) models through simulation studies and is compared to moment estimation via the seasonal Yule-Walker equations. Applicability of the technique is demonstrated through an analysis of a seasonal stream-flow series from the Rio Caroni River in Venezuela.

Additional publication details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
Maximum likelihood estimation for periodic autoregressive moving average models
Series title:
Technometrics
DOI:
10.1080/00401706.1985.10488076
Volume:
27
Issue:
4
Year Published:
1985
Language:
English
Publisher:
Taylor & Francis
Description:
10 p.
First page:
375
Last page:
384