On Markov-switching periodic ARMA models

ABSTRACT

In this work, we propose a generalization of the classical Markov-switching ARMA models to the periodic time-varying case. Specifically, we propose a Markov-switching periodic ARMA (MS-PARMA) model. In addition of capturing regime switching often encountered during the study of many economic time series, this new model also captures the periodicity feature in the autocorrelation structure. We first provide some probabilistic properties of this class of models, namely the strict periodic stationarity and the existence of higher-order moments. We thus propose a procedure for computing the autocovariance function where we show that the autocovariances of the MS-PARMA model satisfy a system of equations similar to the PARMA Yule–Walker equations. We propose also an easily implemented algorithm which can be used to obtain parameter estimates for the MS-PARMA model. Finally, a simulation study of the performance of the proposed estimation method is provided.

KEYWORDS:

• Higher-order moments
• Markov-switching models
• maximum-likelihood method
• MS-PARMA models
• periodic ARMA model
• periodic stationarity.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62M10
• 62M05

Acknowledgments

The authors are deeply grateful to the Editor in Chief and to the referees for their careful reading, useful remarks and constructive suggestions that substantially improved the quality of the paper.