Pure-birth INARCH Models

Abstract

This article illustrates the connection between a time series of counts and pure birth processes. The Poisson INARCH(1) model is frequently rejected in real-world applications. A plausible explanation for this is that the Poisson process is a pure birth process characterized by constant rates. Generally, the conditional distributions of a time series of counts—whether they are over-dispersed, under-dispersed, or equidispersed—are

associated with pure birth processes that have either unequal (monotonic or non-monotonic) or equal rates. Therefore, we propose a new INARCH(1) model featuring conditional unequal-rate and equal-rate distributions. This streamlined model is applied to the time series of strike counts and significantly outperforms the Poisson INARCH(1) model as well as other conventional models found in the literature.