On the robustness of Mann-Kendall tests used to forecast critical transitions

Non-parametric approaches to test for trends in time series make use of the Mann-Kendall statistic. Based on asymptotic arguments, these tests assume that its distribution follows a Gaussian distribution, even for autocorrelated time series. Recent results on the lack of validity of this assumption urge a robustness analysis of these approaches. While the issue is relevant across a wide range of applications, we illustrate it here in the context of detecting early warning signals (EWS) of critical transitions, which are used across a variety of research domains, and where commonly applied methods generate autocorrelation. We present a broad analysis, covering all types of critical transitions commonly investigated in EWS studies. We compare empirical distributions of the Mann-Kendall statistic computed from classical EWS indicators preceding critical transitions to the theoretical distributions hypothesized by Mann-Kendall tests. We detect mismatches leading to inflated type I error rates, which would routinely lead to announcing a critical transition while it is not occurring. In contrast to a recent recommendation, we conclude that the use of Mann-Kendall tests for trend detection in the context of forecasting critical transitions should be avoided. We point out several alternative methods available instead.