A covariate-driven beta-binomial integer-valued GARCH model for bounded counts with an application

This paper considers the modeling problem of the weekly number of districts with new cases of cryptosporidiosis infection, and proposes a covariate-driven beta-binomial integer-valued GARCH model with a logit transformation to illustrate such bounded integer-valued time series data with extra-binomial variation and high volatility. We establish the existence of the stationary and ergodic solution by imposing a contraction condition on its conditional mean process and a Markov structure on the incorporated covariate process, consider the conditional maximum likelihood (CML) estimator for the parameter vector and discuss its asymptotic properties, conduct a simulation study to examine the finite sample performance of the CML estimator for the proposed model with three data generating mechanisms of the covariate process. Finally, an application to the weekly number of districts with new cases of cryptosporidiosis infection is considered to illustrate the superior performance of the proposed model.