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Abstract
We study different approaches for modelling intervention effects in time series of counts, focusing on the so-called integer-valued GARCH models. A previous study treated 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 its occurrence, but not the underlying mean, and then also enters the dynamics of the process. While the former definition describes an internal change of the system, 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 model misspecification and computational issues.
Acknowledgements
The research of R. Fried, P. Kerschke and T. Liboschik was supported by the German Research Foundation (DFG, SFB 823 ‘Statistical modelling of nonlinear dynamic processes’). The authors thank Professor A. Latour for kindly providing the campylobacterosis data. The first author thanks the Department of Mathematics and Statistics of the University of Cyprus for their hospitality during his two visits. The authors thank two anonymous reviewers for their helpful comments.