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Integer-valued GARCH process. (English) Zbl 1150.62046
The authors propose a simple model as an integer-valued analogue of the generalized autoregressive conditional heteroskedastic (GARCH(\(p,q\))) model with Poisson deviates. Putting particular emphasis to the case \(p=1, q=1\), it is shown, from a second-order point of view, that this integer-valued GARCH process is a standard ARMA(1,1) process. The problem of maximum likelihood estimation of the parameters is investigated and the asymptotic distribution of the estimators is derived. A numerical example and an application of this model to real time series are presented.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F10 Point estimation
62E20 Asymptotic distribution theory in statistics
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