Some ARMA models for dependent sequences of poisson counts
- 1 March 1988
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 20 (04) , 822-835
- https://doi.org/10.1017/s0001867800018395
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 of n consecutive 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 14 references indexed in Scilit:
- The distributional structure of finite moving-average processesJournal of Applied Probability, 1988
- 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
- Discrete Analogues of Self-Decomposability and StabilityThe Annals of Probability, 1979
- ASPECTS OF CORRELATION IN BIVARIATE POISSON DISTRIBUTIONS AND PROCESSESAustralian Journal of Statistics, 1979
- A Time Series Approach to Queueing Systems with Applications for Modeling Job-Shop In-Process InventoriesManagement Science, 1977
- On Infinitely Divisible Random VectorsThe Annals of Mathematical Statistics, 1957