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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.15230 |
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| _version_ | 1866908970672717824 |
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| author | Gamot, Tristan Thibeau--Sutre, Nils Van Dooren, Tom J. M. |
| author_facet | Gamot, Tristan Thibeau--Sutre, Nils Van Dooren, Tom J. M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15230 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the robustness of Mann-Kendall tests used to forecast critical transitions Gamot, Tristan Thibeau--Sutre, Nils Van Dooren, Tom J. M. Applications 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. |
| title | On the robustness of Mann-Kendall tests used to forecast critical transitions |
| topic | Applications |
| url | https://arxiv.org/abs/2604.15230 |