Hostname: page-component-77c89778f8-n9wrp Total loading time: 0 Render date: 2024-07-17T18:40:20.687Z Has data issue: false hasContentIssue false
  • English
  • Français

An Analysis of Poisson Moving-Average Processes

Published online by Cambridge University Press:  27 July 2009

William P. McCormick  and
YouSung Park
William P. McCormick
Affiliation:
Department of Statistics, University of Georgia, Athens, Georgia 30602
YouSung Park
Affiliation:
Department of Statistics, Korea University, Seoul, 136-701, Korea
Get access Rights & Permissions [Opens in a new window]

Abstract

Al-Osh and Alzaid (1988, Statistical Papers 29: 281–300) introduced a class of Poisson moving-average processes. In this paper, we analyze certain properties of such models. In particular, we show that the model has the property of time reversibility. Regression properties of the model are also given. Furthermore, we determine the asymptotic limit distribution for the sample autocovariance function and establish the asymptotic validity of a bootstrap approximation.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 11 , Issue 4 , October 1997 , pp. 487 - 507
Copyright
Copyright © Cambridge University Press 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Al-Osh, M.A. & Alzaid, A.A. (1988). Integer-valued moving average (INMA) process. Statistical Papers 29: 281–300.CrossRefGoogle Scholar
2.Al-Osh, M.A. & Alzaid, A.A. (1992). First-order autoregressive time series with negative binomial and geometric marginals. Communications on Statistical Theory and Methods 21: 2483–2492.CrossRefGoogle Scholar
3.Alzaid, A.A. & Bouzar, N. (1994). On some integer-valued autoregressive moving average models. Journal of Multivariate Analysis 50: 132–151.Google Scholar
4.Alzaid, A.A. & Al-Osh, M.A. (1990). An integer-valued pth-order autoregressive structure (INAR(p)) process. Journal of Applied Probability 27: 314–324.CrossRefGoogle Scholar
5.Bickel, P.J. & Freedman, D.A. (1981). Some asymptotic theory for the bootstrap. Annals of Statistics 9: 1196–1217.CrossRefGoogle Scholar
6.Jacobs, P.A. & Lewis, P.A.W. (1978). Discrete time series generated by mixtures I: Correlational and runs properties. Journal of the Royal Statistical Society B 40: 94–105.Google Scholar
7.Jacobs, P.A. & Lewis, P.A.W. (1978). Discrete time series generated by mixtures II: Asymptotic properties. Journal of the Royal Statistical Society B 40: 222–228.Google Scholar
8.Jacobs, P.A. & Lewis, P.A.W. (1983). Stationary discrete autoregressive moving average time series generated by mixtures. Journal of Time Series Analysis 4: 18–36.CrossRefGoogle Scholar
9.McKenzie, E. (1986). Autoregressive moving-average processes with negative-binomial and geometric marginal distributions. Advances in Applied Probability 18: 679–705.CrossRefGoogle Scholar
10.McKenzie, E. (1988). Some ARMA models for dependent sequences of Poisson counts. Advances in Applied Probability 20: 822–835.CrossRefGoogle Scholar