Integer-Valued GARCH Process

René Ferland (1) , Alain Latour (2) , Driss Oraichi (3)

1 DMS - Département de Mathématiques et de statistique [UdeM- Montréal]
2 LABSAD - Laboratoire de Statistiques et Analyse des Données
3 Centre de recherche du CHU Sainte-Justine / Research Center of the Sainte-Justine University Hospital [Montreal, Canada]

An integer-valued analogue of the classical GARCH$(p,q)$ model with Poisson deviates is proposed and a condition for the existence of such a process is given. For the case $p=1$, $q=1$, it is explicitly shown that an integer-valued GARCH process is a standard ARMA$(1, 1)$ process. The problem of maximum likelihood estimation of parameters is treated. An application of the model to a real time series with a numerical example is given.

Mots clés: Integer-valued time series; Garch model

Domaines: Statistiques [math.ST]

René Ferland, Alain Latour, Driss Oraichi. Integer-Valued GARCH Process. Journal of Time Series Analysis, 2006, 27 (6), pp.923-942. ⟨hal-00319793⟩