Modeling extreme values of processes observed at irregular time steps: Application to significant wave height

This work is motivated by the analysis of the extremal behavior of buoy and satellite data describing wave conditions in the North Atlantic Ocean. The available data sets consist of time series of significant wave height (Hs) with irregular time sampling. In such a situation, the usual statistical m...

Full description

Bibliographic Details
Published in:The Annals of Applied Statistics
Main Authors: Raillard, Nicolas, Ailliot, Pierre, Yao, Jianfeng
Format: Article in Journal/Newspaper
Language:English
Published: Inst Mathematical Statistics 2014
Subjects:
Online Access:https://archimer.ifremer.fr/doc/00218/32888/31372.pdf
https://doi.org/10.1214/13-AOAS711
https://archimer.ifremer.fr/doc/00218/32888/
Description
Summary:This work is motivated by the analysis of the extremal behavior of buoy and satellite data describing wave conditions in the North Atlantic Ocean. The available data sets consist of time series of significant wave height (Hs) with irregular time sampling. In such a situation, the usual statistical methods for analyzing extreme values cannot be used directly. The method proposed in this paper is an extension of the peaks over threshold (POT) method, where the distribution of a process above a high threshold is approximated by a maxstable process whose parameters are estimated by maximizing a composite likelihood function. The efficiency of the proposed method is assessed on an extensive set of simulated data. It is shown, in particular, that the method is able to describe the extremal behavior of several common time series models with regular or irregular time sampling. The method is then used to analyze Hs data in the North Atlantic Ocean. The results indicate that it is possible to derive realistic estimates of the extremal properties of Hs from satellite data, despite its complex space–time sampling.