Spatial Extreme Value Analysis using Point Processes

Abstract

Extreme value theory is a field in statistics dealing with the occurrence of rare events, also known as extreme events. It is commonly found in financial applications, but also when modeling rare environmental events. This Master’s thesis proposes a new methodology for modeling spatio-temporal extreme values, by generalising a method for extremes of a time series to both space and time. The method is applied to data of extreme wildfire activity in the United States, with the goal to predict the risk of wildfires exceeding some large threshold. The model created for predicting extreme wildfires in the spatio-temporal dimension is created from a self-exciting model, with previous events triggering new events. In the spatio-temporal dimension, the self-excitation is dependant on both the time and the distance to previous events, making point processes suitable for modeling these. The resulting model manages to capture both the influence of previous wildfires, as well as the impact of a regions vegetation when assessing the risk of large wildfires in the area. While the model cannot predict the exact locations of all wildfires at a selected time point, it accurately shows the regions with an elevated risk of extensive wildfire activity. It also captures the trend of increasing wildfire activity in the studied area.