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The distributional structure of finite moving-average processes

Published online by Cambridge University Press:  14 July 2016

ED McKenzie
ED McKenzie*
Affiliation:
University of Strathclyde
*
∗Postal address: Department of Mathematics, University of Strathclyde, Livingstone Tower, 26 Richmond St., Glasgow G1 1XH, UK.
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Abstract

Analysis of time-series models has, in the past, concentrated mainly on second-order properties, i.e. the covariance structure. Recent interest in non-Gaussian and non-linear processes has necessitated exploration of more general properties, even for standard models. We demonstrate that the powerful Markov property which greatly simplifies the distributional structure of finite autoregressions has an analogue in the (non-Markovian) finite moving-average processes. In fact, all the joint distributions of samples of a qth-order moving average may be constructed from only the (q + 1)th-order distribution. The usefulness of this result is illustrated by references to three areas of application: time-reversibility; asymptotic behaviour; and sums and associated point and count processes. Generalizations of the result are also considered.

Keywords

MOVING-AVERAGE PROCESSESNON-GAUSSIAN PROCESSESJOINT DISTRIBUTIONSTIME-REVERSIBILITYCOUNTING PROCESSMOVING-MINIMUM PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 2 , June 1988 , pp. 313 - 321
Copyright
Copyright © Applied Probability Trust 1988 

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