An integer-valued pth-order autoregressive structure (INAR(p)) process
- 1 June 1990
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 27 (02) , 314-324
- https://doi.org/10.1017/s0021900200038766
Abstract
An extension of the INAR(1) process which is useful for modelling discrete-time dependent counting processes is considered. The model investigated here has a form similar to that of the Gaussian AR(p) process, and is called the integer-valued pth-order autoregressive structure (INAR(p)) process. Despite the similarity in form, the two processes differ in many aspects such as the behaviour of the correlation, Markovian property and regression. Among other aspects of the INAR(p) process investigated here are the limiting as well as the joint distributions of the process. Also, some detailed discussion is given for the case in which the marginal distribution of the process is Poisson.Keywords
This publication has 6 references indexed in Scilit:
- Some ARMA models for dependent sequences of poisson countsAdvances in Applied Probability, 1988
- First‐Order Integer‐Valued Autoregressive (INAR (1)) Process: Distributional and Regression PropertiesStatistica Neerlandica, 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