在统计学和时间序列分析中，长期记忆性(LongMemory)是指时间序列数据在时间上具有持久的相关性，过去的观测值对未来的影响持续存在。研究发现，在很多实际应用中，例如金融时间序列、地球物理学数据等，不符合传统的独立同分布假设，而是具有长期相关性。

而变点问题一直以来都是统计学和数据分析领域的热门话题。其主要研究时间序列中某些特定时刻发生突变的位置和性质，这些突变可能代表了系统结构的变化或外部因素的影响。解决变点问题有助于本文更好地理解数据的变化趋势和性质。而且在实际应用中，时间序列数据往往存在多个变点。且变点的个数是不可知的。因此本文围绕非监督前提下，长记忆时间序列的多变点检验的问题展开讨论。具体内容如下：

相对于经典的累积和统计量，本文采用了自正则方法构造统计量研究长记忆序列的多变点检验问题。均值变点检验中，理论证明本文的自正则构造统计量在原假设下的极限分布为分数布朗运动，在备择假设下证明了该统计量的一致性。并且数值模拟的结果也表明，并且随着样本变点个数的增加，自正则的统计量相对于传统的累计和统计量在经验功效方面也表现出相对稳定的结果。

鉴于实际应用中还需要检验类似的其他一维变点(如中位数变点等)的情况，基于均值的自正则统计量，本文也构造了针对其他一维变点的统计量，并推导了在原假设和备择假设下的极限分布。同时针对上述统计量计算量大的缺陷进行优化，提出了基于比值的优化统计量。最后，选取了1981年至2006年间全球范围热带气旋风力变化和2018年至2022年道琼斯指数变化数据进一步验证了文章提出的自正则统计量的合理性和有效性。

In statistics and time series analysis, long memory refers to the phenomenon where time series data exhibit persistent correlations over time, meaning past observations have a lasting impact on future values. Research has shown that in many practical applications, such as financial time series and geophysical data, the data do not conform to the traditional assumption of independent and identically distributed (i.i.d.) observations, but instead exhibit long-term correlations.

Change point detection has always been a popular topic in statistics and data analysis. It primarily studies the locations and nature of abrupt changes at certain specific points in time series data. These changes may represent structural changes in the system or the influence of external factors. Solving change point problems helps to better understand the trends and characteristics of data changes. Moreover, in practical applications, time series data often contain multiple change points, and the number of change points is unknown. Therefore, this paper discusses the problem of multiple change point detection in long memory time series under an unsupervised framework. The specific content is as follows:

Compared to the classic cumulative sum statistics, this paper adopts a self-normalization method to construct statistics for the multiple change point detection problem in long memory series. In mean change point detection, the theoretical proof shows that the self-normalized constructed statistic follows a fractional Brownian motion under the null hypothesis and proves the consistency of the statistic under the alternative hypothesis. Numerical simulation results also indicate that, as the number of change points in the sample increases, the self-normalized statistic exhibits relatively stable empirical power compared to traditional cumulative sum statistics.

Considering that practical applications also require testing for other one-dimensional change points (such as median change points), this paper constructs statistics for other one-dimensional change points based on the self-normalized mean statistic and derives the asymptotic distribution under the null and alternative hypotheses. Additionally, to address the computational burden of the aforementioned statistics, an optimized statistic based on the ratio is proposed. Finally, the proposed self-normalized statistics' rationality and effectiveness are further validated using global tropical cyclone wind speed data from 1981 to 2006 and Dow Jones Index data from 2018 to 2022..

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