On double-switching ARMA processes

Amel Zerari; Ahmed Ghezal; Imane Zemmouri

doi:10.5269/bspm.67889

Amel Zerari University Centre Abdelhafid Boussouf Mila: Centre Universitaire Abdelhafid Boussouf Mila
Ahmed Ghezal Department of Mathematics and Computer Sciences, University Center of Mila, Algeria.
Imane Zemmouri Department of Mathematics, University of Annaba, Elhadjar 23, Annaba, Algeria.

Abstract

In this paper, we introduce a double-switching ARMA model, in which the observed process is an ARMA model subject to Markov switching and a periodic sequence of period s₂. We give conditions for the existence of periodic stationary solutions of the double-switching ARMA and higher-order moments of such solutions in the general vector specification. We provide an expression in closed-form of the autocovariance function of this process and its higher power and therefore admit ARMA representation.

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