Comparison of trend detection methods in GEV models

Abstract

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.

Keywords:

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

MATHEMATICAL SUBJECT CLASSIFICATION:

• 62G32
• 62F40
• 60G70
• 62M10

Acknowledgments

The authors are grateful to Steve Taylor from Pacific Forestry Centre, Canadian Forest Service for providing the real data from BC Wildfire Service, Ministry of Lands, Forests, and Natural Resource Operations.

Additional information

Funding

The project was supported by the European Union, co-financed by the European Social Fund (EFOP-3.6.3-VEKOP-16-2017-00002).