A Two-Stage Framework of Weighted Nonparametric Single Change-Point Tests and Copula Models for Extreme Temperature Analysis in Upper Northern Thailand

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This study examines two weighted (variance-standardized) versions of classical nonparametric single change-point tests, the weighted Pettitt (W-Pet-CP) and weighted Cramér–von Mises (W-CvM-CP) tests, in which the change-point process is divided by w(τ)=(τ/n)(1−τ/n) to reduce the loss of detection ability for changes near the ends of a series. We derive their limiting null distributions and their behavior under fixed and local location and scale alternatives, and compare them, using Monte Carlo simulation, with the Pettitt, Cramér–von Mises, Mood and Lepage change-point tests. Both weighted tests kept the nominal type I error and markedly improved the ability to locate changes near the boundaries, and W-CvM-CP and Lepage-CP were the only procedures that were effective for both location and scale shifts. In a second stage, the tests were applied to annual maximum (Tmax) and minimum (Tmin) temperatures and their difference (D=Tmax−Tmin) at eight stations in upper northern Thailand (1957–2025 at six stations and 1981–2025 at two), with false-discovery-rate control and field-significance testing, and copula models were fitted to the joint behavior of Tmax and Tmin. After multiplicity adjustment, upward shifts in Tmin of 1.6–3.1 °C were detected at all eight stations, mostly around 1987 and 1999, whereas Tmax shifted significantly only at Mae Hong Son (1982) and Lampang (1978). Decreases in D, clustered around 1999, were regionally significant under the independence assumption but less robust to serial correlation. The dependence between Tmax and Tmin was weak (Kendall’s |τK|≤0.21) and vanished after the detected shifts were removed, so copula-based joint return periods are reported with bootstrap confidence intervals and interpreted with caution.

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Related topics: Climate variability and models · Advanced Statistical Process Monitoring · Climate Change and Environmental Impact