Model Averaging of Integer-Valued Autoregressive Model With Covariates

This article considers model averaging in the class of the integer-valued autoregressive (INAR) processes. The INAR process is a class of structural models that can be used to model dependent count data in fields such as medicine, economics, finance and marketing. It specifies the data generating process (DGP) via the distributions of certain thinning and arrival processes instead of an approximate multiplicative and additive relationship, which means that maximum likelihood (ML) is a natural candidate for estimation. Forecasts can not only be evaluated in terms of points and intervals but also through the entire forecast distribution. Here, we propose a K-fold cross-validation model averaging (KCVMA) estimator based on ML and prove that the KCVMA estimator is asymptotically optimal in a metric equivalent to a squared loss criterion. The KCVMA estimators are consistent, provided at least one candidate model is not underfitted. The probabilistic nature of the INAR process also enables us to conduct probabilistic forecasts based on the KCVMA estimator. Monte Carlo simulations and empirical analysis show that the KCVMA estimator can improve forecast accuracy over existing model averaging and model selection methods