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Statistical measures of extremal dependence illustrated using measured sea surface elevations from a neighbourhood of coastal locations

Research output: Contribution to journalJournal article

Published

Journal publication date1/04/2013
JournalOcean Engineering
Volume62
Number of pages10
Pages68-77
Early online date28/02/13
Original languageEnglish

Abstract

The extremal dependence of stationary time-series at pairs of locations can be summarised using one or more of a number of statistics. We illustrate the application of the coefficient of tail dependence, the $\chi$ and $\bar{\chi}$ statistics, and the conditional extremes model of Heffernan--Tawn to estimate the extremal dependence in time-series of 3-hour maxima of sea surface elevation across a spatial array of measurement gauges at the US Army Corps of
Engineers' Field Research Facility on the Atlantic coast of North Carolina. Although the original data are non-stationary, we induce stationarity on a site-by-site basis using a non-parametric model to remove the mean trend. Subsequently, we find that pairs of locations are generally asymptotically dependent. Parameter estimates for the Heffernan--Tawn model, although uncertain, suggest that
characteristics of conditional extremes vary systematically with distance from the conditioning site.