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.

中文翻译：

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监测计数的双变量时间序列模型的参数变化

在本研究中，我们考虑采用在线监测程序来检测双变量计数时间序列的参数变化，遵循双变量整数值广义自回归异方差（BIGARCH）和自回归（BINAR）模型。为了解决这个问题，我们采用从这些模型获得的（标准化）残差构建的累积和（CUSUM）过程。为了达到控制极限，我们为建议的监控过程开发了极限定理。进行了仿真研究和实际数据分析，以验证所提出方法的有效性。