On Computationally-Scalable Spatio-Temporal Regression Clustering of Precipitation Threshold Excesses

TL;DR

This paper introduces a scalable spatio-temporal clustering method for precipitation threshold excesses using local GPD models and a nonparametric switching process, effectively handling missing covariates and nonstationarity.

Contribution

It presents a novel FEM-BV-GPD approach that models complex nonstationary behavior without strong prior assumptions, improving analysis of precipitation extremes.

Findings

Effective clustering of precipitation extremes demonstrated on Swiss data.

Outperforms standard methods in capturing nonstationary behavior.

Provides a flexible, data-driven framework for spatio-temporal extreme value analysis.

Abstract

Focusing on regression based analysis of extremes in a presence of systematically missing covariates, this work presents a data-driven spatio-temporal regression based clustering of threshold excesses. It is shown that in a presence of systematically missing covariates the behavior of threshold excesses becomes nonstationary and nonhomogenous. The presented approach describes this complex behavior by a set of local stationary Generalized Pareto Distribution (GPD) models, where the parameters are expressed as regression models, and a latent spatio-temporal switching process. The spatio-temporal switching process is resolved by the nonparametric Finite Element Methodology for time series analysis with Bounded Variation of the model parameters (FEM-BV). The presented FEM-BV-GPD approach goes beyond strong a priori assumptions made in standard latent class models like Mixture Models and Hidden Markov Models. In addition, it provides a pragmatic description of the underlying dependency structure. The performance of the framework is demonstrated on historical precipitation data for Switzerland and compared with the results obtained by the standard methods on the same data.