Modeling and inferences for bounded multivariate time series of counts

Abstract

This paper considers modeling bounded multivariate time series of counts and the inferential procedures of this model. For modeling, we introduce a hybrid type model similar to the scheme of integer-valued autoregressive (INAR) and conditional autoregressive heteroscedastic (INARCH) models. To estimate the model parameters, we use the conditional least squares estimator (CLSE) and minimum density power divergence estimator (MDPDE). To evaluate the small sample performances of the proposed estimators, we conduct a Monte Carlo simulation study and demonstrate that the proposed methods work well. Real data analysis is also carried out using syphilis data in the U.S. for illustration.