Dynamic model averaging adapted to dynamic regression models for time series of counts

Abstract

There is an extensive literature on observation-driven approaches for count time series. Their deterministic parameter-updating procedure, based on lagged dependent variables, leads to closed-form likelihoods and simple estimation procedures, and this has propelled their popularity and the development of computational tools for practitioners. On the contrary, in parameter-driven models of count time series, the parameters vary over time as dynamic processes with random innovations following a given model and their flexibility and generality make them attractive. However, the analytical expressions for the likelihood have no closed form and the estimation procedures require complex computer-intensive algorithms since they demand the evaluation of multiple integrals. The innumerous computational and inferential difficulties inherent to this model class have prevented the development and availability of software that would make possible their widespread applicability. In this study, we develop a parameter-driven method for count time series that includes models that allow for overdispersion and/or zero inflation. Additionally, we account for model uncertainty by using dynamic model averaging, which allows the posterior model probabilities to change over time. Other important features of the proposed methodology are its mathematical and computational simplicity allied to its extremely fast algorithms compared with the latest available methods.