Modelling interventions in INGARCH processes

Abstract

We study different approaches to describe intervention effects within the framework of integer-valued GARCH (INGARCH) models for time series of counts. Fokianos and Fried (J. Time Ser. Anal. 2010, 31: 210–225) treat a model where an intervention affects the non-observable underlying mean process at the time point of its occurrence and additionally the whole process thereafter via its dynamics. As an alternative, we consider a model where an intervention directly affects the observation at the time point of its occurrence, but not the underlying mean, and then also enters the dynamics of the process. While the former definition describes an internal change, the latter can be understood as an external effect on the observations due to e.g. immigration. For our alternative model we develop conditional likelihood estimation and, based on this, tests and detection procedures for intervention effects. Both models are compared analytically and using simulated and real data examples. We study the effect of misspecification on the fitted intervention model. Special attention is paid to computational issues.