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Mixing properties of integer-valued GARCH processes. (English) Zbl 1464.62380

Summary: We consider models for count variables with a GARCH-type structure. Such a process consists of an integer-valued component and a volatility process. Using arguments for contractive Markov chains we prove that this bivariate process has a unique stationary regime. Furthermore, we show absolute regularity (\(\beta\)-mixing) with geometrically decaying coefficients for the count process. These probabilistic results are complemented by a statistical analysis and a few simulations.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
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References:

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