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An integer-valued pth-order autoregressive structure (INAR(p)) process

Published online by Cambridge University Press:  14 July 2016

A. A. Alzaid  and
M. Al-osh
A. A. Alzaid
Affiliation:
King Saud University
M. Al-osh*
Affiliation:
King Saud University
*
∗Postal address for both authors: Department of Statistics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia.
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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

INTEGER-VALUED RANDOM VARIABLEAUTOCORRELATIONREGRESSIONLIMITING AND JOINT DISTRIBUTIONSSTATE SPACE REPRESENTATIONPOISSON INAR(p) PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 2 , June 1990 , pp. 314 - 324
Copyright
Copyright © Applied Probability Trust 1990 

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References

Al-Osh, M. A. and Alzaid, A. A. (1987) First order integer-valued autoregressive (INAR(1)) process. J. Time Series Anal. 8, 261–275.Google Scholar
Al-Osh, M. A. and Alzaid, A. A. (1988) Integer-valued moving average (INMA) process. Statistische Hefte 29, 281–300.Google Scholar
Alzaid, A. A. and Al-Osh, M. A. (1988) First order integer-valued autoregressive process: distributional and regression properties. Statist. Nederlandica 42, 53–61.Google Scholar
Fuller, W. A. (1976) Introduction to Statistical Time Series. Wiley, New York.Google Scholar
Harvey, A. C. and Phillips, G. D. A. (1979) Maximum likelihood estimation of regression models with autoregressive-moving average disturbances. Biometrika 66, 49–58.Google Scholar
Heathcote, C. R. (1966) A branching process allowing immigration. J. R. Statist. Soc. B. 28, 213–217.Google Scholar
Mckenzie, E. (1985) Some simple models for discrete variate time series. Water Res. Bull. 21, 645–650.CrossRefGoogle Scholar
Mckenzie, E. (1986) Autoregressive moving-average processes with negative binomial and geometric marginal distributions. Adv. Appl. Prob. 18, 679–705.Google Scholar
Mckenzie, E. (1988) Some ARMA models for dependent sequences of Poisson counts. Adv. Appl. Prob. 20, 822–835.Google Scholar
Steutel, F. W. and Van, Harn. K. (1986) Discrete operator self-decomposability and queueing networks. Commun. Statist. Stoch. Models 2, 161–169.Google Scholar
Steutel, F. W. and Van, Harn. K. (1987) Queueing networks and operator-self decomposability. Preprint.Google Scholar