Modeling nonstationary extremes of storm severity: Comparing parametric and semiparametric inference

Abstract

This article compares the modeling of nonstationary extreme events using parametric models with local parametric and semiparametric approaches also motivated by extreme value theory. Specifically, three estimators are compared based on (a) (local) semiparametric moment estimation, (b) (local) maximum likelihood estimation, and (c) spline‐based maximum likelihood estimation. Inference is performed in a sequential manner, highlighting the synergies between the different approaches to estimating extreme quantiles, including the T‐year level and right endpoint when finite. We present a novel heuristic to estimate nonstationary extreme value threshold with exceedances varying on a circular domain, and hypothesis‐testing procedures for identifying max‐domain of attraction in the nonstationary setting. Bootstrapping is used to estimate nonstationary confidence bounds throughout. We provide step‐by‐step guides for estimation, and explore the different inference strategies in application to directional modeling of hindcast storm peak significant wave heights recorded in the North Sea.

Applications of large deviation theory in geophysical fluid dynamics and climate science

“…The possibility of establishing accurate climatologies of, e.g., heatwaves and cold spells in various regions of the globe seems particularly relevant for climate service centres, public agencies and private actors active, for example, in the energy and in agricultural sectors as well as in finance, and re-insurances. Indeed, in order to achieve full real-life applicability in the context of the presence of the seasonal cycle and of a changing climate, the results presented in this paper should be extended in such a way to incorporate the case of non-stationary time series of observables of non-autonomous dynamical systems, along the lines of what has been proposed in the context of EVT [47,84,145,189,194]. This is another great example of a very fruitful meeting point between applied and basic research.…”

A penalised piecewise-linear model for non-stationary extreme value analysis of peaks over threshold

“…We expect these sources of non-stationarity to be adequately characterised in the estimated PPL model. Data from the same location have been considered in Randell et al (2016) and Konzen et al (2021).…”

Applications of large deviation theory in geophysical fluid dynamics and climate science

“…The possibility of establishing accurate climatologies of, e.g., heatwaves and cold spells in various regions of the globe seems particularly relevant for climate service centres, public agencies and private actors active, for example, in the energy and in agricultural sectors as well as in finance, and reinsurances. Indeed, in order to achieve full real-life applicability in the context of the presence of the seasonal cycle and of a changing climate, the results presented in this paper should be extended in such a way to incorporate the case of non-stationary time series of observables of non-autonomous dynamical systems, along the lines of what has been proposed in the context of EVT [33,286,287,288,289]. This is another great example of a very fruitful meeting point between applied and basic research.…”