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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
##### Keywords:
integer-valued time series; GARCH model; heteroskedasticity
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##### References:
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