Modelling Short- and Long-Term Dependencies of Clustered High-Threshold Exceedances in Significant Wave Heights

The peaks-over-threshold (POT) method has a long tradition in modelling extremes in environmental variables. However, it has originally been introduced under the assumption of independently and identically distributed (iid) data. Since environmental data often exhibits a time series structure, this...

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Autores principales:	Pushpa Dissanayake, Teresa Flock, Johanna Meier, Philipp Sibbertsen
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	peaks-over-threshold extremal clustering long-range dependence ARFIMA models extreme value theory significant wave heights Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/42ff30a1664345f2a491018eda4ee6dd
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spelling	oai:doaj.org-article:42ff30a1664345f2a491018eda4ee6dd2021-11-11T18:20:47ZModelling Short- and Long-Term Dependencies of Clustered High-Threshold Exceedances in Significant Wave Heights10.3390/math92128172227-7390https://doaj.org/article/42ff30a1664345f2a491018eda4ee6dd2021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2817https://doaj.org/toc/2227-7390The peaks-over-threshold (POT) method has a long tradition in modelling extremes in environmental variables. However, it has originally been introduced under the assumption of independently and identically distributed (iid) data. Since environmental data often exhibits a time series structure, this assumption is likely to be violated due to short- and long-term dependencies in practical settings, leading to clustering of high-threshold exceedances. In this paper, we first review popular approaches that either focus on modelling short- or long-range dynamics explicitly. In particular, we consider conditional POT variants and the Mittag–Leffler distribution modelling waiting times between exceedances. Further, we propose a new two-step approach capturing both short- and long-range correlations simultaneously. We suggest the autoregressive fractionally integrated moving average peaks-over-threshold (ARFIMA-POT) approach, which in a first step fits an ARFIMA model to the original series and then in a second step utilises a classical POT model for the residuals. Applying these models to an oceanographic time series of significant wave heights measured on the Sefton coast (UK), we find that neither solely modelling short- nor long-range dependencies satisfactorily explains the clustering of extremes. The ARFIMA-POT approach, however, provides a significant improvement in terms of model fit, underlining the need for models that jointly incorporate short- and long-range dependence to address extremal clustering, and their theoretical justification.Pushpa DissanayakeTeresa FlockJohanna MeierPhilipp SibbertsenMDPI AGarticlepeaks-over-thresholdextremal clusteringlong-range dependenceARFIMA modelsextreme value theorysignificant wave heightsMathematicsQA1-939ENMathematics, Vol 9, Iss 2817, p 2817 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	peaks-over-threshold extremal clustering long-range dependence ARFIMA models extreme value theory significant wave heights Mathematics QA1-939
spellingShingle	peaks-over-threshold extremal clustering long-range dependence ARFIMA models extreme value theory significant wave heights Mathematics QA1-939 Pushpa Dissanayake Teresa Flock Johanna Meier Philipp Sibbertsen Modelling Short- and Long-Term Dependencies of Clustered High-Threshold Exceedances in Significant Wave Heights
description	The peaks-over-threshold (POT) method has a long tradition in modelling extremes in environmental variables. However, it has originally been introduced under the assumption of independently and identically distributed (iid) data. Since environmental data often exhibits a time series structure, this assumption is likely to be violated due to short- and long-term dependencies in practical settings, leading to clustering of high-threshold exceedances. In this paper, we first review popular approaches that either focus on modelling short- or long-range dynamics explicitly. In particular, we consider conditional POT variants and the Mittag–Leffler distribution modelling waiting times between exceedances. Further, we propose a new two-step approach capturing both short- and long-range correlations simultaneously. We suggest the autoregressive fractionally integrated moving average peaks-over-threshold (ARFIMA-POT) approach, which in a first step fits an ARFIMA model to the original series and then in a second step utilises a classical POT model for the residuals. Applying these models to an oceanographic time series of significant wave heights measured on the Sefton coast (UK), we find that neither solely modelling short- nor long-range dependencies satisfactorily explains the clustering of extremes. The ARFIMA-POT approach, however, provides a significant improvement in terms of model fit, underlining the need for models that jointly incorporate short- and long-range dependence to address extremal clustering, and their theoretical justification.
format	article
author	Pushpa Dissanayake Teresa Flock Johanna Meier Philipp Sibbertsen
author_facet	Pushpa Dissanayake Teresa Flock Johanna Meier Philipp Sibbertsen
author_sort	Pushpa Dissanayake
title	Modelling Short- and Long-Term Dependencies of Clustered High-Threshold Exceedances in Significant Wave Heights
title_short	Modelling Short- and Long-Term Dependencies of Clustered High-Threshold Exceedances in Significant Wave Heights
title_full	Modelling Short- and Long-Term Dependencies of Clustered High-Threshold Exceedances in Significant Wave Heights
title_fullStr	Modelling Short- and Long-Term Dependencies of Clustered High-Threshold Exceedances in Significant Wave Heights
title_full_unstemmed	Modelling Short- and Long-Term Dependencies of Clustered High-Threshold Exceedances in Significant Wave Heights
title_sort	modelling short- and long-term dependencies of clustered high-threshold exceedances in significant wave heights
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/42ff30a1664345f2a491018eda4ee6dd
work_keys_str_mv	AT pushpadissanayake modellingshortandlongtermdependenciesofclusteredhighthresholdexceedancesinsignificantwaveheights AT teresaflock modellingshortandlongtermdependenciesofclusteredhighthresholdexceedancesinsignificantwaveheights AT johannameier modellingshortandlongtermdependenciesofclusteredhighthresholdexceedancesinsignificantwaveheights AT philippsibbertsen modellingshortandlongtermdependenciesofclusteredhighthresholdexceedancesinsignificantwaveheights
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Modelling Short- and Long-Term Dependencies of Clustered High-Threshold Exceedances in Significant Wave Heights

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