Modelling interventions in INGARCH processes
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Date
2013-01-28
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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.
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Keywords
change-point detection, generalised linear models, level shifts, outliers, time series of counts, transient shifts