Interventions in INGARCH processes

We study the problem of intervention effects generating various types of outliers in a linear count time‐series model. This model belongs to the class of observation‐driven models and extends the class of Gaussian linear time‐series models within the exponential family framework. Studies about effects of covariates and interventions for count time‐series models have largely fallen behind, because the underlying process, whose behaviour determines the dynamics of the observed process, is not observed. We suggest a computationally feasible approach to these problems, focusing especially on the detection and estimation of sudden shifts and outliers. We consider three different scenarios, namely the detection of an intervention effect of a known type at a known time, the detection of an intervention effect when the type and the time are both unknown and the detection of multiple intervention effects. We develop score tests for the first scenario and a parametric bootstrap procedure based on the maximum of the different score test statistics for the second scenario. The third scenario is treated by a stepwise procedure, where we detect and correct intervention effects iteratively. The usefulness of the proposed methods is illustrated using simulated and real data examples.