Applicability of prewhitening to eliminate the influence of serial correlation on the Mann‐Kendall test

TLDR

Prewhitening has been used to mitigate serial correlation in Mann‑Kendall trend tests for hydrological series, yet its effectiveness remains poorly documented. This study evaluates the efficacy of prewhitening for eliminating serial correlation effects on the Mann‑Kendall test through Monte Carlo simulation. Simulated time series incorporated a linear trend and a lag‑1 autoregressive (AR(1)) noise component. Results show that serial correlation’s impact on the Mann‑Kendall test depends on sample size, correlation magnitude, and trend strength; when sample size and trend are large, serial correlation has negligible effect, but prewhitening can either attenuate or inflate trend, leading to increased false negatives or positives, rendering it unsuitable when a trend is present.

Abstract

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.