Integer‐Valued GARCH Process

TLDR

The authors propose an integer‑valued analogue of the classical GARCH(p, q) model with Poisson deviates and establish a condition for its existence. The model is constructed as an integer‑valued GARCH analogue using Poisson innovations, extending the standard GARCH framework to count data. For the case p = 1, q = 1, the integer‑valued GARCH process reduces to a standard ARMA(1, 1) process. Abstract.

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.