Ergodic Estimation and Model Assessment for Dynamic Exceedance Times

Abstract

This article concerns the estimation of hitting time statistics for potentially non-stationary processes. The main focus is exceedance times of environmental processes. To this end we consider an empirical estimator based on ergodic theory under the assumption that the considered process is a deterministic transformation of some ergodic process. This estimator is empirically analysed and rigorous convergence results, including a central limit theorem, are covered. Using our estimator, we compute confidence intervals for mean exceedance times of empirical wind data. This serves as a baseline for assessing the performance of several models in terms of predicted mean exceedance time. Special attention is given to the model class known as Gaussian copula processes, which models the environmental process as a deterministic, possibly time-dependent, transformation of a stationary parent Gaussian process.