On Mixture Periodic Vector Autoregressive Models

Abstract

This article deals with the study of some properties of a mixture periodically correlated n-variate vector autoregressive (MPVAR) time series model, which extends the mixture time invariant parameter n-vector autoregressive (MVAR) model that has been recently studied by Fong et al. (2007). Our main contributions here are, on the one side, the obtaining of the second moment periodically stationary condition for a n-variate MPVAR_S(n; K; 2, …, 2) model; furthermore, the closed-form of the second moment is obtained and, on the other side, the estimation, via the Expectation-Maximization (EM) algorithm, of the coefficient matrices and the error variance matrix.

Keywords:

• EM algorithm
• Mixture periodic vector AR models
• Multivariate Periodically correlated process
• Periodic vector autoregressive models

Mathematics Subject Classification:

• 62F12; 62M10

Acknowledgments

The authors present their most sincere thanks and their deep gratitude to Prof. N. Balakrishnan, Editor-in-Chief, for his helps and continued encouragements. Also, they present to the anonymous referee their most sincere thanks and profound acknowledgments for the helpful suggestions, constructive comments, and many important corrections that have allowed us to improve the quality and the readability of the article.