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Integer-Valued GARCH Process

Authors


Alain Latour, LabSAD, Université Pierre Mendès-France, Bâtiment Sciences Humaines et Mathématiques, Campus Universitaire de St-Martin d'Hères, 1251, Avenue Centrale; B.p. 47 - 38 040 Grenoble Cedex 9, France. E-mail: Alain.Latour@upmf-grenoble.fr

Abstract

Abstract.  An integer-valued analogue of the classical generalized autoregressive conditional heteroskedastic (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 autoregressive moving average (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.

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