## 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

### MSC:

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