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Spectral Factorization of Periodically Correlated MA(1) Processes

Part of: Inference from stochastic processes Convergence and divergence of infinite limiting processes

Published online by Cambridge University Press:  14 July 2016

Mohamed Bentarzi  and
Marc Hallin
Mohamed Bentarzi*
Affiliation:
Université des Sciences et Techniques d'Alger
Marc Hallin*
Affiliation:
Université Libre de Bruxelles
*
∗Postal address: Institut de Mathématiques, Université des Sciences et Techniques d'Alger, B.P. 9 Dar El Beida, Alger, Algeria
∗∗Postal address: Institut de Statistique, Université Libre de Bruxelles, cp 210, B1050 Bruxelles, Belgium
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Abstract

The spectral factorization problem, i.e. the problem of obtaining all possible MA representations of a process with given autocovariance function, is considered for univariate, d-periodic MA(1) (equivalently, 1-dependent in the second-order sense) processes. The solutions are provided explicitly, and their invertibility properties are investigated. A characterization, in terms of their autocovariance functions, of non-invertible d-periodic 1-dependent processes, extending to the periodic case the traditional unit root condition, is provided.

Keywords

Periodic modelsmoving average modelsinvertibility

MSC classification

Primary: 62M10: Time series, auto-correlation, regression, etc. 40A15: Convergence and divergence of continued fractions
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 1 , March 1998 , pp. 46 - 54
Copyright
Copyright © Applied Probability Trust 1998 

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