Existence and Stochastic Structure of a Non‐negative Integer‐valued Autoregressive Process

Abstract

A simple criterion is given for the existence of a generalized integer‐valued autoregressive (GINAR(p)) process. We show that the GINAR(p) process is nothing but an AR(p) process. The spectral density gives a good insight into the stochastic structure of a GINAR(p) model. The spectral representation of the process is explicitly given. The estimation of parameters of the process is also discussed and clarifies some results presented by Du and Li (The integer‐valued autoregressive (INAR(p)) model. J. Times Ser. Anal., 12 (1991), 129‐‐42). Finally, we describe the number of seizures of an epileptic patient using a model of this class.