Estimating function method for nonnegative autoregressive models

A stationary sequence of nonnegative random variables generated by autoregressive (AR) models may be used to describe the inter-arrival times between events in counting processes. Even though, several such models are available in the literature, there is no unified approach to estimate their parameters. In this paper, we propose a class of combined estimating function method to estimate the model parameters of AR models with gamma marginals. The proposed method is compared with other estimation procedures and are illustrated by simulation and data analysis.