Monitoring parameter change for bivariate time series models of counts

In this study, we consider an online monitoring procedure to detect a parameter change for bivariate time series of counts, following bivariate integer-valued generalized autoregressive heteroscedastic (BIGARCH) and autoregressive (BINAR) models. To handle this problem, we employ the cumulative sum (CUSUM) process constructed from the (standardized) residuals obtained from those models. To attain control limits, we develop limit theorems for the proposed monitoring process. A simulation study and real data analysis are conducted to affirm the validity of the proposed method.