Modified Mann-Kendall with Higher-Order Statistics for Trend Analysis

Abstract Trend analysis of rainfall events is crucial, especially in understanding changes in precipitation patterns over time, which can have significant implications for climate adaptation planning. The Mann-Kendall (MK) trend test is preferred by researchers, given its robustness in handling non-normal data with extreme out-liers. However, the assumption of independence is often not fulfilled. Researchers have begun proposing modifications to MK to enhance its interpretability when dealing with positive autocorrelation. Nevertheless, the issue of nonlinearity, where future values of time series data cannot be explained by a linear function, is not widely discussed. In this paper, a modified MK named Mann-Kendall with Third-Order Cumulant (MKC3) is proposed. A simulation study was conducted using MKC3, with comparisons made against MK and Mann-Kendall Rank Detrended (MKRD), alongside a case study of rainfall in Peninsular Malaysia. The simulation results reveal that MK, MKRD, and MKC3 are comparable, with MK suitable for independent data, MKRD for strongly autocorrelated data, and MKC3 for bilinear, nonlinear and sinusoidal models. The case study shows increasing trends for rainfall in the Northeast Monsoon (NEM) and decreasing trends in the Southwest Monsoon (SWM). Overall, the MKC3 is justified by its robustness, but the selection remains a trade-off.