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Time series models with univariate margins in the convolution-closed infinitely divisible class

Part of: Inference from stochastic processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Harry Joe
Harry Joe*
Affiliation:
University of British Columbia
*
∗Postal address: Department of Statistics, The University of British Columbia, 6356 Agricultural Road, Vancouver, British Columbia, Canada V6T 1Z2.
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Abstract

A unified way of obtaining stationary time series models with the univariate margins in the convolution-closed infinitely divisible class is presented. Special cases include gamma, inverse Gaussian, Poisson, negative binomial, and generalized Poisson margins. ARMA time series models obtain in the special case of normal margins, sometimes in a different stochastic representation. For the gamma and Poisson margins, some previously defined time series models are included, but for the negative binomial margin, the time series models are different and, in several ways, better than previously defined time series models. The models are related to multivariate distributions that extend a univariate distribution in the convolution-closed infinitely divisible class. Extensions to the non-stationary case and possible applications to modelling longitudinal data are mentioned.

Keywords

NON-NORMAL TIME SERIESINFINITELY DIVISIBLECOUNT DATANEGATIVE BINOMIAL

MSC classification

Primary: 60G10: Stationary processes
Secondary: 62M10: Time series, auto-correlation, regression, etc.
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 3 , September 1996 , pp. 664 - 677
Copyright
Copyright © Applied Probability Trust 1996 

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