An integer-valued p th-order autoregressive structure (INAR(p)) process. (English) Zbl 0704.62081

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


62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60G12 General second-order stochastic processes
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