Some ARMA models for dependent sequences of poisson counts
- 1 December 1988
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 20 (4) , 822-835
- https://doi.org/10.2307/1427362
Abstract
A family of models for discrete-time processes with Poisson marginal distributions is developed and investigated. They have the same correlation structure as the linear ARMA processes. The joint distribution ofnconsecutive observations in such a process is derived and its properties discussed. In particular, time-reversibility and asymptotic behaviour are considered in detail. A vector autoregressive process is constructed and the behaviour of its components, which are Poisson ARMA processes, is considered. In particular, the two-dimensional case is discussed in detail.Keywords
This publication has 17 references indexed in Scilit:
- The distributional structure of finite moving-average processesJournal of Applied Probability, 1988
- FIRST‐ORDER INTEGER‐VALUED AUTOREGRESSIVE (INAR(1)) PROCESSJournal of Time Series Analysis, 1987
- Autoregressive moving-average processes with negative-binomial and geometric marginal distributionsAdvances in Applied Probability, 1986
- Discrete operator-selfdecomposabiuty and queueing networksCommunications in Statistics. Stochastic Models, 1986
- SOME SIMPLE MODELS FOR DISCRETE VARIATE TIME SERIES1Jawra Journal of the American Water Resources Association, 1985
- STATIONARY DISCRETE AUTOREGRESSIVE‐MOVING AVERAGE TIME SERIES GENERATED BY MIXTURESJournal of Time Series Analysis, 1983
- First-order autoregressive gamma sequences and point processesAdvances in Applied Probability, 1980
- ASPECTS OF CORRELATION IN BIVARIATE POISSON DISTRIBUTIONS AND PROCESSESAustralian Journal of Statistics, 1979
- A Multiple Time Series Approach to Modeling the Manufacturing Job-Shop as a Network of QueuesManagement Science, 1977
- On Infinitely Divisible Random VectorsThe Annals of Mathematical Statistics, 1957