On the performance of information criteria for model identification of count time series

Abstract

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.

INARMA Modeling of Count Time Series

“…The obtained numbers of model selections (out of 1000 replications) are tabulated in Appendix B.2. Some of the conclusions found by Weiß and Feld [23] are confirmed also here. The BIC's ability for identifying the correct model always improves with increasing T, whereas the AIC for the smallest model, i.e., for the INAR(1) model in our comparison, stabilizes at a rate below 80%.…”

“…These criteria are computed together with the ML estimation of each candidate model, and that model is selected as the final one which minimizes the value of AIC or BIC, respectively. More details on these and further ICs can be found in Neath and Cavanaugh [21], Cavanaugh and Neath [22], Weiß and Feld [23]. In Weiß and Feld [23], the performance of these criteria was analyzed for count time series mainly generated by regression-type DGPs.…”

“…More details on these and further ICs can be found in Neath and Cavanaugh [21], Cavanaugh and Neath [22], Weiß and Feld [23]. In Weiß and Feld [23], the performance of these criteria was analyzed for count time series mainly generated by regression-type DGPs. They confirmed the consistency of the BIC in their study, but the actual rates of correct model identifications for smaller sample sizes T were often best for the AIC.…”

“…Since model selection across INARMA models was not considered in Weiß and Feld [23], we also analyzed the AIC's and BIC's performance in our simulation study. For this purpose, we used all of the six considered models as possible candidate models for any of the simulated count time series.…”

Models for autoregressive processes of bounded counts: How different are they?

“…However, little is known about such an ability in nonnested and nonlinear time series models for counts (Jung et al 2016). Two recent studies, Weiß and Feld (2020) and Weiß et al (2019), partially follow the direction outlined by Jung et al (2016), but concentrate on the case of unbounded counts. Diop and Kenge (2020) propose a penalized criterion relying on a Poisson quasi-likelihood approach for some INGARCH-type processes of counts, and they prove its consistency under certain regularity conditions.…”