中文摘要：

研究具有无穷方差的厚尾相依序列均值存在变点的问题。采用Ratio检验法研究序列在原假设无变点及备择假设存在一个变点的假设检验问题,首先基于残差的累积和函数建立检验统计量,在适当的假设条件下,给出检验统计量在原假设下的极限分布,并对统计量的一致性检验进行了推导证明,最后通过数值模拟验证Ratio检验法的有效性。

英文摘要：

In order to study change point in the mean of heavy-tailed dependent sequence under the null hypothesis of no change against the alternative hypothesis of change point, the ratio test statistic based on residual cumulative sum functionals is given. Under some proper assumption, the limiting distribution of the test under the null hypothesis is derived and the consistence of the test is also obtained. Finally, the results of Monte Carlo is shown to support the argument.