Estimating return levels from serially dependent extremes

Abstract

In this paper, we investigate the relationship between return levels of 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, and peaks over thresholds analyses 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 the extremal index is estimated appropriately—using all threshold 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.