Applicability of prewhitening to eliminate the influence of serial correlation on the Mann‐Kendall test
Applicability of prewhitening to eliminate the influence of serial correlation on the Mann‐Kendall test
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DOI：
10.1029/2001wr000861
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发表时间：
2002-06
影响因子：
5.4
通讯作者：
S. Yue;C. Y. Wang
中科院分区：
文献类型：
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作者：
S. Yue;C. Y. Wang
在水文时间序列趋势检测研究中，预白化已被用于消除序列相关性对Mann - Kendall （MK）检验的影响。然而，它完成这一任务的能力并没有得到很好的证明。本文采用蒙特卡罗模拟方法对这一问题进行了研究。模拟时间序列由一个线性趋势和一个滞后自回归（AR(1)）过程和噪声组成。仿真结果表明，当时间序列中存在趋势时，正/负序列相关对MK检验的影响取决于样本量、序列相关大小和趋势大小。当样本量和趋势量足够大时，序列相关性不再显著影响MK检验统计量。通过预白化从时间序列中去除正AR(1)将去除一部分趋势，从而降低拒绝零假设的可能性，而零假设可能是错误的。相反，通过预白化去除负AR(1)会膨胀趋势，导致拒绝原假设的可能性增加，而原假设可能是正确的。因此，当一个时间序列内存在趋势时，预白化不适用于消除序列相关对MK检验的影响。
Prewhitening has been used to eliminate the influence of serial correlation on the Mann‐Kendall (MK) test in trend‐detection studies of hydrological time series. However, its ability to accomplish such a task has not been well documented. This study investigates this issue by Monte Carlo simulation. Simulated time series consist of a linear trend and a lag 1 autoregressive (AR(1)) process with a noise. Simulation results demonstrate that when trend exists in a time series, the effect of positive/negative serial correlation on the MK test is dependent upon sample size, magnitude of serial correlation, and magnitude of trend. When sample size and magnitude of trend are large enough, serial correlation no longer significantly affects the MK test statistics. Removal of positive AR(1) from time series by prewhitening will remove a portion of trend and hence reduces the possibility of rejecting the null hypothesis while it might be false. Contrarily, removal of negative AR(1) by prewhitening will inflate trend and leads to an increase in the possibility of rejecting the null hypothesis while it might be true. Therefore, prewhitening is not suitable for eliminating the effect of serial correlation on the MK test when trend exists within a time series.