Model fitting for count time series is of great relevance for many economic applications. Here, we focus on the step of model selection, where information criteria like AIC and BIC are commonly used in practice. Previous studies about their model selection abilities concentrated on real-valued time series, but here, we comprehensively investigate AIC and BIC in a count time series context. In our simulations, we consider diverse scenarios of model selection, like the identification of serial (in)dependence, overdispersion, zero inflation or a trend, the order selection within a given model family as well as the model selection also across model families. We apply our findings to economic count time series about monthly numbers of strikes in the US, and about monthly numbers of corporate insolvencies in the districts of Rhineland-Palatinate.
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