Novel bivariate integer-valued autoregressive models: theory, estimation, and a comparative study of machine learning approaches

This study presents two novel bivariate integer-valued autoregressive models of order one. The proposed models demonstrate superior performance compared to some existing BINAR(1) models, as evidenced by commonly used information criteria. To estimate the model parameters, two distinct estimation methods are employed, and the performance of these estimators is assessed through Monte Carlo simulation studies. In the empirical analysis, three count time series datasets are examined using two complementary approaches: traditional statistical modelling and modern machine learning techniques. The findings underscore the advantages and limitations of each method, offering valuable insights for selecting appropriate models in count time series applications.