从上世纪七十年代，变点问题就是计量经济学中的热门话题之一，变点理论和实践运用也受到了普遍重视。变点的存在直接影响序列的分布特征，故检验结构变点对构建更精确的时间序列模型变得十分重要。由于厚尾序列呈“尖峰厚尾”的特征，并且数据间也往往具有相依性，均值是时间序列数据的主要数值特征。基于此，本文运用Block Bootstrap抽样方法对厚尾相依序列均值变点问题展开研究，内容如下：

    厚尾指数为(1,2)时，采用最小二乘估计方法，构造稳健Ratio统计量研究新息过程为AR(p)的厚尾模型的均值变点。在合理的假设和引理下，从理论上推导出了统计量在原假设下的极限分布及证明了其在备择假设下的一致性。但是发现原Ratio的检验效果易受变点位置的影响，变点发生在前半段的经验势高于变点发生在后半段的经验势。基于此，考虑对统计量加以颠倒，得出颠倒统计量，然后再取原统计量和颠倒统计量的最大值，从而理论上证实了修正统计量的经验势对变点时刻不再敏感。由于序列间具有一定程度的相依性，且统计量的临界值与厚尾指数有关，所以采用Block Bootstrap抽样方法模拟出更加准确的临界值。最后，通过有限样本下的数值模拟可以得出，修正统计量能够有效检验均值变点，也证明了该方法的可行性。

    厚尾指数为(0,1)时，采用M估计方法研究新息过程为AR(1)的厚尾序列的均值变点。当厚尾指数较小时，序列的“奇异点”会增加并且此时不存在期望，所以最小二乘估计的检验作用就会减弱，从而提出了M估计方法。根据广义的中心极限定理，基于M估计推导出统计量在原假定下的极限分布，进而确定了它们在备择假设下的一致性。有限样本下的数值模拟表明，不同参数下统计量的临界值相对稳定，原假设下的经验水平在0.05上下浮动，备择假设下的经验势也随着样本量和跳跃幅度的增大而提高。所以当异常数据较多时，M估计比最小二乘法构建的统计量更为稳健。

    Since the 1970s, the change point problem has been one of the hot topics in econometrics.  The theory and practical application of change points have attracted widespread attention. The change point directly affects the distribution characteristics of the series. In order to build a more accurate time series model, so it is very important for testing the structural point . Since heavy-tailed series are characterized by "spikes and heavy tails", and the data are often dependent on each other. The mean  is also the main numerical characteristic of time series data. Based on the characteristic, this paper uses Block Bootstrap sampling method to detect the mean-change point under heavy-tailed model. The detailed content is as follows.

     When the heavy-tailed index is (1,2), this paper adopts the least squares estimation method to construct a robust ratio statistic for detecting the mean change points, and the innovation process is AR(p). Under reasonable assumptions and lemmas, the limiting distribution of the test statistic under the null hypothesis and its consistency under the alternative hypothesis are theoretically derived. However, it is found that the test effect of the original Ratio is easily affected by the location of the change point, and the empirical potential of the change point occurring in the first half of the period is higher than that of the change point occurring in the second half of the period. Based on the defect, the statistic was reversed to derive the reversal statistic, and then the maximum of the original statistic and the reversal statistic was taken. Thus theoretically confirming that the empirical potential of the revised statistic is no longer sensitive to the moment of the change point. Since there is a certain degree of inter-series dependence and the critical value of the statistic is related to the heavy-tailed index, the Block Bootstrap sampling method is used to simulate a more accurate critical value. Finally, numerical simulations with limited samples can conclude that the modified statistic can effectively test the mean change point, which also proves the feasibility of the method.

    When the heavy-tailed index is (0,1), this paper adopts the M-estimation method to study the mean change point of the heavy-tailed series with the innovation process as AR(1). When the heavy-tailed index is small, the number of the singularity becomes more and the series has no expectation, so least squares estimation will be weakened. Thus the M estimation method is proposed. Based on the generalized central limit theorem, the limiting distributions of the statistics under the null hypothesis are derived, and their consistency under the alternative hypothesis is determined. Numerical simulations under finite samples show that the critical values of the statistics for different parameters are relatively stable, the empirical size under the null hypothesis fluctuates around 0.05, and the empirical potential under the alternative hypothesis also increases with the increase of the sample size and the jump magnitude. Therefore, when there are more anomalous data, the M estimation is more robust than the statistic constructed by the least squares method.

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