Modified Mann-Kendall with higher-order statistics for trend analysis

Trend analysis of rainfall events is important to understand changes in precipitation patterns over time, which may affect climate adaptation planning. The Mann-Kendall (MK) trend test is preferred by researchers for its robustness in handling non-normal data with extreme outliers. However, the assumption of independence is often not fulfilled. Modifications have been introduced to improve MK performance under autocorrelation, but the issue of nonlinearity is still not widely discussed. In this study, a modified MK called Mann-Kendall with Third-Order Cumulant (MKC3) is proposed. A simulation study was conducted with comparisons made against MK and other MK variants to provide practical guidance for practitioners, followed by a case study of rainfall in Peninsular Malaysia. The results show that MK, TFPW, SMK, MKRD, and MKC3 have different strengths: MK for independent data, TFPW preserves trends in autocorrelated series, SMK performs well for weak autocorrelation with small sample size, MKRD is robust for strong autocorrelation and sinusoidal models, and MKC3 performs well in bilinear and nonlinear models. The case study shows increasing trends during the Northeast Monsoon (NEM) and decreasing trends during the Southwest Monsoon (SWM). Overall, MKC3 shows promising robustness, but the selection remains a trade-off.