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Model-Building Problem of Periodically Correlatedm-Variate Moving Average Processes

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  • Bentarzi, Mohamed

Abstract

The model-building problem of periodically correlatedm-variateq-dependent processes is considered. We show that for a given periodical autocovariance function of anm-variateMA(q) process there are two particular corresponding classes (that may reduce to one class) of periodic (equivalent) models. Furthermore, any other (intermediate) model is not periodic. It is, however, asymptotically periodic. The matrix coefficients of the particular periodic models are given in terms of limits of some periodic matrix continued fractions, which are a generalization of the classical periodic continued fractions (Wall, 1948). These periodic matrix continued fractions are particular solutions of some prospective and/or retrospective recursion equations, arising from the symbolic factorization of the associated linear autocovariance operator. In addition, we establish a procedure to calculate these limits. Numerical examples are given for the simple cases of periodically correlated univariate one- and two-dependent processes.

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  • Bentarzi, Mohamed, 1998. "Model-Building Problem of Periodically Correlatedm-Variate Moving Average Processes," Journal of Multivariate Analysis, Elsevier, vol. 66(1), pages 1-21, July.
    • Handle: RePEc:eee:jmvana:v:66:y:1998:i:1:p:1-21
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    1. Aknouche, Abdelhakim & Guerbyenne, Hafida, 2009. "On some probabilistic properties of double periodic AR models," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 407-413, February.
    2. Aknouche, Abdelhakim & Bentarzi, Mohamed, 2008. "On the existence of higher-order moments of periodic GARCH models," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3262-3268, December.

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