Some ARMA models for dependent sequences of poisson counts
作者： Ed Mckenzie
DOI: 10.2307/1427362
关键词: Autoregressive–moving-average model 、 Binomial distribution 、 Applied mathematics 、 Time reversibility 、 Marginal distribution 、 Mathematics 、 Compound Poisson process 、 Joint probability distribution 、 Statistics 、 Poisson distribution 、 Autoregressive model
摘要: 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.
jstor.org
sci-hub.se 参考文章(22)
Ed McKenzie, AUTOREGRESSIVE MOVING-AVERAGE PROCESSES WITH NEGATIVE-BINOMIAL AND GEOMETRIC MARGINAL DISTRIBUTIONS Advances in Applied Probability. ,vol. 18, pp. 679- 705 ,(1986) , 10.2307/1427183
ED McKenzie, The distributional structure of finite moving-average processes Journal of Applied Probability. ,vol. 25, pp. 313- 321 ,(1988) , 10.1017/S002190020004095X
Patricia A. Jacobs, Peter A. W. Lewis, Discrete Time Series Generated by Mixtures Ii: Asymptotic Properties Journal of the Royal Statistical Society: Series B (Methodological). ,vol. 40, pp. 222- 228 ,(1978) , 10.1111/J.2517-6161.1978.TB01667.X
A. J. Lawrance, P. A. W. Lewis, The Exponential Autoregressive-Moving Average Earma(P,Q) Process Journal of the Royal Statistical Society: Series B (Methodological). ,vol. 42, pp. 150- 161 ,(1980) , 10.1111/J.2517-6161.1980.TB01112.X
Chin Long Chiang, An introduction to stochastic processes and their applications R. E. Krieger. ,(1980)
P. A. Jacobs, P. A. W. Lewis, Discrete Time Series Generated by Mixtures. I: Correlational and Runs Properties Journal of the Royal Statistical Society: Series B (Methodological). ,vol. 40, pp. 94- 105 ,(1978) , 10.1111/J.2517-6161.1978.TB01653.X
F. W. Steutel, W. Vervaat, S. J. Wolfe, INTEGER-VALUED BRANCHING PROCESSES WITH IMMIGRATION Advances in Applied Probability. ,vol. 15, pp. 713- 725 ,(1983) , 10.1017/S0001867800021571
Ed. McKenzie, SOME SIMPLE MODELS FOR DISCRETE VARIATE TIME SERIES Journal of the American Water Resources Association. ,vol. 21, pp. 645- 650 ,(1985) , 10.1111/J.1752-1688.1985.TB05379.X
D. P. Gaver, P. A. W. Lewis, First Order Autoregressive Gamma Sequences and Point Processes. Advances in Applied Probability. ,vol. 12, pp. 727- 745 ,(1980) , 10.2307/1426429
Gideon Weiss, TIME-REVERSIBILITY OF LINEAR STOCHASTIC PROCESSES Journal of Applied Probability. ,vol. 12, pp. 831- 836 ,(1975) , 10.2307/3212735