Assessing Extrapolation of Peaks Over Thresholds with Martingale Testing

TL;DR

This paper introduces a robust, simple approach for estimating the probability of rare extreme precipitation events using Extreme Value Theory and martingale testing to evaluate extrapolation accuracy.

Contribution

It proposes a novel use of martingale testing to assess and select high quantile levels in extreme value analysis, enhancing extrapolation reliability.

Findings

Martingale testing effectively evaluates extrapolation power.

The approach successfully estimated extreme precipitation probabilities.

The method offers a new perspective on agnostic model selection in EVT.

Abstract

We present the winning strategy for the EVA2025 Data Challenge, which aimed to estimate the probability of extreme precipitation events. These events occurred at most once in the dataset making the challenge fundamentally one of extrapolating extreme values. Given the scarcity of extreme events, we argue that a simple, robust modeling approach is essential. We adopt univariate models instead of multivariate ones and model Peaks Over Thresholds using Extreme Value Theory. Specifically, we fit an exponential distribution to model exceedances of the target variable above a high quantile (after seasonal adjustment). The novelty of our approach lies in using martingale testing to evaluate the extrapolation power of the procedure and to agnostically select the level of the high quantile. While this method has several limitations, we believe that framing extrapolation as a game opens the door to other agnostic approaches in Extreme Value Analysis.