MIXTURE PERIODIC AUTOREGRESSION WITH PERIODIC ARCH ERRORS

Mohamed Bentarzi (Algeria) and Fayçal Hamdi (Algeria)

Received October 6, 2007

Abstract

This paper explores some basic properties of mixture periodic autoregression with periodic ARCH errors (MPAR-ARCH), extending the MAR-ARCH model of Wong and Li [10], to capture the periodicity feature in the autocorrelation structure exhibited by many nonlinear time series. Our main focus is to provide the first and second moment periodic stationary conditions of this model. Furthermore, conditions for the existence of the fourth moments are established for some particular interesting cases. Closed-forms of these moments are obtained. MLE is carried out via the iterative EM algorithm, performance of which is shown via a simulation.

Keywords and phrases: mixture periodic autoregressive conditionally heteroskedastic models, periodically correlated process, periodically stationary condition, EM algorithm.