Metrika ( IF 0.7 ) Pub Date : 2021-08-02 , DOI: 10.1007/s00184-021-00834-1 Mamadou Lamine Diop 1 , William Kengne 1
We consider together the retrospective and the sequential change-point detection in a general class of integer-valued time series. The conditional mean of the process depends on a parameter \(\theta ^*\) which may change over time. We propose procedures which are based on the Poisson quasi-maximum likelihood estimator of the parameter, and where the updated estimator is computed without the historical observations in the sequential framework. For both the retrospective and the sequential detection, the test statistics converge to some distributions obtained from the standard Brownian motion under the null hypothesis of no change and diverge to infinity under the alternative; that is, these procedures are consistent. Some results of simulations as well as real data application are provided.
中文翻译:
Poisson QMLE 用于一般整数值时间序列模型中的变化点检测
我们一起考虑一般整数值时间序列类中的回顾性和顺序变化点检测。该过程的条件均值取决于参数\(\theta ^*\),该参数可能随时间变化。我们提出了基于参数的泊松准最大似然估计量的程序,其中更新的估计量是在没有顺序框架中的历史观察的情况下计算的。对于回顾性和顺序性检测,检验统计量收敛到在无变化的原假设下从标准布朗运动得到的一些分布,在替代下发散到无穷大;也就是说,这些程序是一致的。提供了一些模拟结果以及实际数据应用。