一类长记忆时间序列趋势项变点的Wilcoxon秩检验

对一类带Hurst指数的分数布朗运动趋势项变点的检验问题进行了研究，提出了一种先对观测序列做一阶差分，再基于差分序列构造Wilcoxon秩统计量做检验的后验检验方法。在原假设下证得检验统计量的极限分布是标准分数布朗运动的泛函，并给出了检验统计量的临界值。数值模拟结果表明，提出的检验方法除Hurst值较大外，均能很好地控制经验水平，经验势随样本量的增多几乎能趋近于1，且在样本量较大时，对截距项变点和方差变点稳健。采用该方法分析了1854—1989年北半球月均气温数据，未检测到趋势项变点。

Wilcoxon rank test for change point in trend in a class of long memory time series

The problem of testing the change point in trend for a class of fractional Brownian motion with Hurst exponent is studied, and a posterior testing method is proposed which firstly makes first-order difference to the observation sequence and then constructs Wilcoxon rank statistics based on the difference sequence for testing. Under the null hypothesis, it is proved that the limit distribution of the test statistic is a functional of the standard fractional Brownian motion and the critical values of the test statistic are given. The numerical simulation results show that the test method proposed in this paper can control the empirical size well except for the case where the Hurst value is too large, and the empirical power can almost be close to 1 following the increase of sample size. Moreover, the method is robust to the intercept change point and variance change point when the sample size is large. Finally, a set of monthly temperature data in the northern hemisphere is analyzed, it is found that there is no change point in trend.