Trend detection in GEV models

Abstract

In recent environmental studies extreme events have a great impact. The yearly and monthly maxima of environment related indices can be analysed by the tools of extreme value theory. For instance, the monthly maxima of the fire weather index in British Columbian forests might be modelled by GEV distribution, but the stationarity of the time series is questionable. This property can lead us to different approaches to test if there is a significant trend in past few years data or not. An approach is a likelihood ratio based procedure which has favourable asymptotic properties, but for realistic sample sizes it might have a large error. In this paper we analyse the properties of the likelihood ratio test for extremes by bootstrap simulations and aim to determine a minimal required sample size. With the theoretical results we re-asses the trends of fire weather index in British Columbian forests.