Alzaid, A. A.; Al-Osh, M. An integer-valued p th-order autoregressive structure (INAR(p)) process. (English) Zbl 0704.62081 J. Appl. Probab. 27, No. 2, 314-324 (1990). An INAR(p) process \(X_ n\) admits the representation \[ X_ n=\sum^{p}_{i=1}\alpha_ i\circ X_{n-i}+\epsilon_ n, \] where \(\epsilon_ n\geq 0\) is an integer-valued white noise and \(\alpha_ i\circ X_{n-i}\) denotes a sum of \(X_{n-i}\) independent 0-1 random variables \(Y_ k\) such that \(P(Y_ k=1)=\alpha_ i\). The authors derive the stationary marginal distribution of \(X_ n\) and the covariance function. The case when \(X_ n\) has a Poisson distribution is discussed in detail. A state space representation of an INAR(p) process is also considered. Reviewer: J.Anděl Cited in 1 ReviewCited in 134 Documents MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 60G12 General second-order stochastic processes Keywords:discrete-time dependent counting processes; integer-valued random variable; autocorrelation; regression; joint distributions; limiting distribution; INAR(p) process; stationary marginal distribution; covariance function; Poisson distribution; state space representation PDFBibTeX XMLCite \textit{A. A. Alzaid} and \textit{M. Al-Osh}, J. Appl. Probab. 27, No. 2, 314--324 (1990; Zbl 0704.62081) Full Text: DOI