由于变点问题的普遍存在性和涉及领域的广泛性，使其成为一个热点问题。均值变点是常见的变点问题之一，受到学者们的广泛重视。大量研究表明，如果忽视时间序列中均值变点的存在往往会产生错误的结论，因此对时间序列进行均值变点检验和估计是非常有必要的。

均值变点常用累积和(Cumulative Sum, CUSUM)统计量来检验，而CUSUM统计量需要估计长期方差，且长期方差的估计量在原假设和备择假设下应满足一致性。事实上，这一条件是很苛刻的，即使在误差项独立的情形下也难以实现。当误差项是相依甚至厚尾相依序列时，估计长期方差就更具有挑战性。为此本文采用两个稳健的Ratio检验统计量有效的避免长期方差估计，讨论了时间序列均值变点检验问题，为CUSUM统计量提供有效的替代方法，具体内容如下：

1) 对于传统的高斯相依时间序列，基于两个稳健统计量讨论了时间序列均值单变点和多变点问题。在原假设下，推导得统计量的渐近分布均是Winner过程的泛函，并在备择假设下，证明统计量的一致性。数值模拟表明，本文的两个统计量所得临界值不受相依系数影响，与Horváth的统计量相比本文统计量的经验水平更逼近显著性水平，经验势也更显著。此外，对于均值多变点检验统计量也具有良好的性能。最后通过中国银行股价和鲁北化工股价两个实例，进一步说明本文方法的有效性和可行性。

2) 鉴于许多经济和金融时间序列数据均具有尖峰、厚尾的特征，已不能用传统的高斯分布描述。因而基于两个修正的Ratio统计量讨论了厚尾AR(p)时间序列均值变点问题，在原假设不存在均值变点的情形下，推导得统计量的渐近分布均是Lévy过程的泛函，并在备择假设存在一个均值变点的情形下证明其一致性。同时，借助Wild Bootstrap重抽样方法有效避免厚尾指数估计进而得到统计量渐近正确的临界值。在均值变点存在的情形下，给出了均值变点位置的估计量，并证明其一致性。数值模拟表明，即使对于小样本，修正统计量也表现出很好的性能。特别的，在原假设下两个统计量的临界值均不受厚尾指数和自回归系数影响；在备择假设下，统计量随变点位置，跳跃幅度等突变因素的变化而变化，但不受偏度系数影响。此外，在原假设下统计量S(k)的经验水平表现出更好的稳健性，而备择假设下统计量M(k)则具备更好的显著性，变点估计量也具有良好的精确性。最后通过上海第一百货股价和尼罗河水流量两组实际数据，进一步说明本文统计量的有效性和可行性。

Because of the universality of change point problem and the extensiveness of related fields, it becomes a hot issue. As one of the common change point problems, the mean change point has been paid more and more attention by scholars. A large number of studies have shown that if the existence of mean change point in time series is ignored, it will often lead to wrong conclusions. Therefore, it is very necessary to test and estimate the mean change point in time series.

The mean change point is often tested by cumulative sum (CUSUM) statistics, which need to estimate the long-term variance, and the estimator of the long-term variance should satisfy the consistency under the null hypothesis and the alternative hypothesis. In fact, this condition is very harsh, even in the case of independent error term is difficult to achieve. Therefore, it is more challenging to estimate the long-term variance when the error terms are dependent or even heavy-tailed dependent sequences. For this reason, this paper adopts two robust Ratio statistics to effectively avoid long-term variance estimation and discusses the change point test of time series mean, providing an effective alternative method for CUSUM test statistics. The specific contents are as follows:

1) For the traditional Gaussian dependent time series, the problem of single and multiple mean change point of time series is discussed based on two robust Ratio test statistics. Under the null hypothesis, the asymptotic distribution of the Ratio statistics is deduced as the functional of Winner process, and the consistency of the statistics is proved under the alternative. Monte Carlo numerical simulation shows that the critical values obtained by the two statistics in this paper are not affected by the dependence coefficient. Compared with Horváth, the empirical size of the statistics in this paper is closer to the significance level, and the empirical power is also more significant. In addition, the statistic also has good performance for multiple mean change point. Finally, the effectiveness and feasibility of this method are further illustrated by two examples of the stock price of Bank of China and Lubei Chemical.

2) Since many economic and financial time series data are characterized by sharp peaks and heavy-tailed, they cannot be described by traditional Gaussian distribution. Then, the mean change point problem of heavy-tailed AR(p) time series is discussed based on two modified Ratio statistics. When there is no mean change point in the null hypothesis, the asymptotic distribution of the derived statistics are all functional of the Lévy process, and its consistency is proved under the condition that there is a mean change-point in the alternative hypothesis. The Wild Bootstrap re-sampling method is used to avoid the estimation of the heavy-tailed index and then the asymptotically correct critical value of the statistics is obtained. As a by-product, the mean change point location estimator is given and its consistency is proved. Monte Carlo numerical simulation shows that even for small samples, the modified statistics show good finite behavior. In particular, the critical values of the two statistics are not affected by the heavy-tailed index and autoregressive coefficient under the null hypothesis. Under the alternative hypothesis, the statistics change with the change point location, change magnitude and other mutation factors, but are not affected by skewness parameters. In addition, the empirical level of statistic S(k) shows better robustness under the null hypothesis, while the statistic M(k) shows better significance under the alternative hypothesis, and the change point estimator also shows good accuracy. Finally, the validity and feasibility of the test statistics in this paper are further illustrated by the stock price of No.1 SDS and the Nile river flow.

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