变点问题是统计学中的一个热点问题，受到了国内外学者的广泛关注。越来越多的实证研究表明，地质、气候、经济等相关数据明显呈现出尖峰厚尾的特点，不能简单的利用高斯分布刻画其统计特征。时间序列的平稳与否决定了构建模型时采取的推断方法，因此应用实际数据建模时需先判定序列的平稳性。基于此，本文主要研究厚尾相依序列的持久性变点的在线监测问题。

在单变点情形下，考虑了厚尾相依序列持久性变点的监测问题。基于M估计，采用滑动比率型统计量，构造了一个稳健的M-Moving Ratio 监测统计量(简称MMR统计量)。基于广义的中心极限定理，推导了MMR统计量在原假设下的极限分布，且证明了从平稳过程(I(0)过程)到非平稳过程(I(1)过程)的变化下该统计量的一致性。针对MMR统计量无法判定从I(1)过程到I(0)过程变化的情况，提出了具备一致性的MMR^-1统计量。数值模拟结果发现：MMR统计量和MMR^-1统计量均不仅很好地控制了原假设下的经验水平，备择假设下有令人满意的的经验势，这表明文中方法能稳健地、快速地检测到持久性变点。最后利用一组滨江集团股票收盘价格数据实证分析，进一步验证了该方法的可行性和有效性。

鉴于观测序列数据的多变点现象经常发生，本文讨论了厚尾相依序列持久性多变点的监测检验。针对多变点问题，提出修正的MMR统计量，推导该统计量在原假设下的渐近分布，给出了备择假设下的发散速度。数值模拟结果表明：经验水平值稳定在显著性水平附近；而经验势随着带宽、厚尾指数的增加而增大。这表明了文中所给的监测方法适用于持久性多变点的检验。最后利用一组京东方A股票收盘价格数据实证分析，进一步验证了该方法的可行性和有效性。

The change point problem is a hot issue in statistics, which has been widely concerned by scholars at home and abroad. More and more empirical studies show that geological, climatic, economic and other related data obviously show the characteristics of peaks and heavy tails, and it is not easy to use Gaussian distribution to describe their statistical characteristics. The stationarity of time series determines the inference method adopted in the construction of the model, so the stationarity of the series should be determined before the application of actual data modeling. Based on this, this paper mainly studies the problem of online monitoring of persistent change points of heavy-tail dependent sequences.

In the case of single change point, the problem of monitoring the persistent change point of heavy-tail dependent sequence is considered. Based on M-estimation, a robust M-moving Ratio monitoring statistic (MMR statistic for short) is constructed by using the moving ratio statistic. Based on the generalized central limit theorem, the limit distribution of the MMR statistic under the null hypothesis is derived, and the consistency of the statistic under the change from stationary process (I(0) process) to non-stationary process (I(1) process) is proved. In view of the fact that MMR statistics cannot determine the change from I(1) process to I(0) process, a consistent MMR^-1 statistic is proposed. The numerical simulation results show that both MMR statistics and MMR^-1 statistics not only well control the empirical sizes under the null hypothesis, but also have satisfactory empirical powers under the alternative hypothesis, which indicates that the method in this paper can detect the persistent change points robustly and quickly. Finally, based on a group of Binjiang Group stock closing price data, the feasibility and effectiveness of this method is verified.

In view of the frequent occurrence of variable points in observed sequence data, this paper discusses the monitoring and testing of persistent change points in heavy-tail dependent sequences. In this paper, a modified MMR statistic is proposed for the problem of change points. The asymptotic distribution of the statistic under the null hypothesis is derived, and the divergence velocity under the alternative hypothesis is given. The numerical simulation results show that the value of empirical sizes is stable around the significance level. The empirical powers increases with the increase of bandwidth and heavy-tail index. This indicates that the method proposed in this paper is suitable for the test of persistent change points. Finally, A group of BOE A stock closing price data is used for empirical analysis to further verify the feasibility and effectiveness of the method.

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