自回归计数时间序列的连续在线监测

Pub Date : 2024-01-02 DOI:10.1007/s42952-023-00247-y
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引用次数: 0

摘要

摘要 本研究探讨了检测计数时间序列参数变化的在线监测问题。为此,我们根据整值广义自回归条件异速(INGARCH)模型得到的残差构建了一个监测过程。由于基于残差或得分向量的 GARCH 类型过程的监控问题可视为马氏差分监控问题的特例,因此我们在使用马氏差分序列的更一般框架内考虑这一问题。在这种一般设置中,研究了停止规则的极限行为,并将其应用于 INGARCH 过程。为了评估我们方法的性能,我们进行了蒙特卡罗模拟。我们还提供了真实数据分析,以作说明。我们的实证研究结果证明了所建议的监控过程的有效性。
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Sequential online monitoring for autoregressive time series of counts

Abstract

This study considers the online monitoring problem for detecting the parameter change in time series of counts. For this task, we construct a monitoring process based on the residuals obtained from integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models. We consider this problem within a more general framework using martingale difference sequences as the monitoring problem on GARCH-type processes based on the residuals or score vectors can be viewed as a special case of the monitoring problems on martingale differences. The limiting behavior of the stopping rule is investigated in this general set-up and is applied to the INGARCH processes. To assess the performance of our method, we conduct Monte Carlo simulations. A real data analysis is also provided for illustration. Our findings in this empirical study demonstrate the validity of the proposed monitoring process.

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