The Predictive Distributions of Thinning-based Count Processes

Overview & Synopsis

This paper shows that the term structure of conditional, or predictive distributions allows for closed form expression in a large family of (possibly higher-order, or infinite order) thinning-based count processes such as INAR(p), INARCH(p), NBAR(p), and INGARCH(1,1). Such predictive distributions are currently often deemed intractable by the literature and existing approximation methods are usually time consuming and induce approximation errors. In this paper, we propose a Taylor's expansion algorithm for these predictive distributions, which is both exact and fast. Through extensive simulation exercises, we demonstrate its advantages with respect to existing methods in terms of the computational gain and/or precision.