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Stationary Time Series Models with Exponential Dispersion Model Margins

Part of: Inference from stochastic processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Bent Jørgensen  and
Peter Xue-Kun Song
Bent Jørgensen*
Affiliation:
University of British Columbia
Peter Xue-Kun Song*
Affiliation:
York University
*
∗Postal address: Department of Statistics, University of British Columbia, 333–6356 Agricultural Road, Vancouver B.C., Canada V6T 1Z2
∗∗Postal address: Department of Mathematics and Statistics, York University, 4700 Keele Street, North York, Ontario, Canada M3J 1P3.
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Abstract

We consider a class of stationary infinite-order moving average processes with margins in the class of infinitely divisible exponential dispersion models. The processes are constructed by means of the thinning operation of Joe (1996), generalizing the binomial thinning used by McKenzie (1986, 1988) and Al-Osh and Alzaid (1987) for integer-valued time series. As a special case we obtain a class of autoregressive moving average processes that are different from the ARMA models proposed by Joe (1996). The range of possible marginal distributions for the new models is extensive and includes all infinitely divisible distributions with finite moment generating functions, hereunder many known discrete, continuous and mixed distributions.

Keywords

Autoregressive processconvolution-closed familyinfinite divisibilitymoving average process of infinite ordernon-normal time seriessaddlepoint approximationsmall-dispersion asymptoticsthinning

MSC classification

Primary: 60G10: Stationary processes
Secondary: 62M10: Time series, auto-correlation, regression, etc.
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 1 , March 1998 , pp. 78 - 92
Copyright
Copyright © Applied Probability Trust 1998 

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Footnotes

Research supported by the Natural Sciences and Engineering Research Council of Canada.

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