Comparison of trend detection methods in GEV models

článek v časopise ve Web of Science, Jimp

en

In recent environmental studies, the examination of extreme events has great impact. The block maxima of environment-related indices can be analyzed by the tools of extreme value theory. For instance, the monthly maxima of the fire weather index at stations in British Columbia might be modeled by GEV distribution, but it is questionable whether the underlying stochastic process is stationary. This property can lead us to different approaches to determine whether there is a significant trend in the past few years’ data or not. One such approach is a likelihood ratio based procedure, which has favorable asymptotic properties, but for realistic sample sizes it might have large decision errors. In this paper, we analyze the properties of the likelihood ratio test for extremes by bootstrap simulations and present a simulation-based procedure to overcome the problem of small sample sizes. We also propose a return level calculation method. Using our theoretical results we reassess the trends of fire weather index monthly maxima in selected stations of British Columbia.

In recent environmental studies, the examination of extreme events has great impact. The block maxima of environment-related indices can be analyzed by the tools of extreme value theory. For instance, the monthly maxima of the fire weather index at stations in British Columbia might be modeled by GEV distribution, but it is questionable whether the underlying stochastic process is stationary. This property can lead us to different approaches to determine whether there is a significant trend in the past few years’ data or not. One such approach is a likelihood ratio based procedure, which has favorable asymptotic properties, but for realistic sample sizes it might have large decision errors. In this paper, we analyze the properties of the likelihood ratio test for extremes by bootstrap simulations and present a simulation-based procedure to overcome the problem of small sample sizes. We also propose a return level calculation method. Using our theoretical results we reassess the trends of fire weather index monthly maxima in selected stations of British Columbia.

Extreme value, Likelihood ratio, Non-stationarity, Return level, Trend

21.09.2020

Taylor & Francis

online

1532-4141

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