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

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 (chi) over bar statistics, and the conditional extremes model of Heffernan-Tawn to estimate the extremal dependence in time-series of 3-h 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. (C) 2013 Elsevier Ltd. All rights reserved.