变点分析主要统计推断观测数据中是否包含结构性的变化，其中持久性变点检验是一个热点研究内容，是指序列存在平稳过程(I(0))与单位根过程(I(1))之间的转化。越来越多的实证数据表明高斯分布不足以刻画其特征，需用重尾分布进行描述。因此，本文研究重尾相依序列下的持久性变点检验，具体内容如下：

       本文将尾指数κ 的研究范围从(1,2)拓展到(0,2)，并利用最小二乘估计构造修正的双侧统计量检验重尾数据下的持久性变点。基于泛函中心极限定理，证明了原假设为单位根过程下统计量的极限分布是稳定过程的泛函；在备择假设下，无论从I(0)变化到I(1)或从I(1)变化到I(0)，统计量均有一致性。由于极限分布依赖于未知的尾指数，采用Block Bootstrap抽样方法以避免尾指数的估计，从而获得精确的临界值。数值模拟结果表明，检验统计量在原假设下有着良好的经验水平值，在备择假设下，当尾指数κ∈(1,2) 时有着令人满意的经验势函数值，当κ∈(0,1) 时统计量的经验势函数值稍有降低。

       为了减弱尾指数，尤其当κ∈(0,1) 时对于统计量检验功效的影响，提出了基于M估计的检验统计量，推导了在原假设下的极限分布仍是稳定过程的泛函；在备择假设下基于M估计统计量的发散速度与基于最小二乘估计统计量的发散速度一致。数值模拟结果表明，基于M估计的检验统计量也有表现良好的经验水平值，在备择假设下的经验势函数值有着显著的提升，尤其在尾指数小于1时其检验功效明显改善。

       当序列为近单位根过程，本文推导了统计量的渐近分布。数值模拟表明在近单位根过程下统计量都是保守的，不会发生“伪拒绝”现象。为进一步说明检验统计量的有效性，采用四组金融数据进行实证分析，结果表明提出的检验方法针对重尾相依序列下的持久性变点检验具有可行性

Change point analysis is mainly used to make statistical inferences about whether the observed data contains structural changes, among which the persistence change test is a hot research content, which refers to the transformation between stationary process (I(0)) and unit root process (I(1)). More and more empirical data show that the Gaussian distribution is not enough to describe its characteristics, so heavy-tailed distribution is needed to describe it. Therefore, this paper studies the persistence change test under heavy-tailed dependent sequences, and the specific contents are as follows:

In this paper, the study range of tail index κ  is extended from (1,2) to (0,2), and based on the least square estimation, a modified two-sided test statistic is constructed to test the persistence change of heavy-tailed dependent sequences. Based on the functional central limit theorem, it is proved that the limit distribution of statistics under the null hypothesis of unit root process is the functional of a stable process. Under the alternative hypothesis, the statistics are consistent regardless of the change from I(0) to I(1) or from I(1) to I(0). Because the limit distribution depends on the unknown tail index, the Block Bootstrap sampling method is used to avoid the estimation of the tail index, so as to obtain the exact critical value. The numerical simulation results show that the test statistic have good empirical size under the null hypothesis. Under the alternative hypothesis, it has a satisfactory experiential potential value when the tail index κ∈(1,2) , and slightly decreases when κ∈(0,1) .

In order to reduce the influence of tail index, especially when κ∈(0,1) , a test statistic based on M-estimation is proposed, and the limit distribution is still the functional of a stable process under the null hypothesis. The divergence rate of the statistics based on M-estimation is consistent with that based on least squares under the alternative hypothesis. The numerical simulation results show that the test statistics based on M-estimation also have good empirical size, and the empirical power under the alternative hypothesis has a significant improvement, especially when the tail index is less than 1, its test efficacy is obviously improved.

When the sequence is a near unit root process, the asymptotic distribution of the statistics is derived. The numerical simulation shows that the statistics are conservative in the near unit root process, and "Over-rejection" phenomenon will not occur. In order to further illustrate the validity of the statistics and methods proposed in this paper, four sets of financial data are used for verification. The results show that the test statistics proposed in this paper are practical for persistence change under heavy-tail dependent sequences.