Estimating return levels from serially dependent extremes

Abstract

In this paper, we investigate the relationship betweenreturn levelsof a process and the strength of serial correlation present in the extremes of that process. Estimates of long period return levels are often used as design requirements, andpeaks over thresholdsanalyses have, in the past, been used to obtain such estimates. However, analyses based on such declustering schemes are extremely wasteful of data, often resulting in great estimation uncertainty represented by very wide confidence intervals. Using simulated data, we show that—provided theextremal indexis estimated appropriately—usingallthreshold excesses can give more accurate and precise estimates of return levels, allowing us to avoid altogether the sometimes arbitrary process of cluster identification. We then apply our method to two data examples concerning sea‐surge and wind‐speed extremes. Copyright © 2012 John Wiley & Sons, Ltd.

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