Saddlepoint approximation for INAR(p) processes

摘要

Saddlepoint techniques have been used successfully in many applications owing to the high accuracy with which they can approximate densities and tail probabilities. We study their use for the estimation of high-order integer-valued autoregressive, INAR(p), processes. Maximum likelihood estimation has been used for the INAR (p) model, but if the order p increases it can become extremely complicated to compute the likelihood, so we propose a saddlepoint approximation which, whilst simple in its application, performs well even in the tails of the distribution and under complicated INAR models. In this paper we consider Poisson innovations. The performance of the approximation is assessed through simulation experiments that show its high accuracy even when maximization of the likelihood function is too hard to be feasible.