Open Access
March 2014 Modeling extreme values of processes observed at irregular time steps: Application to significant wave height
Nicolas Raillard, Pierre Ailliot, Jianfeng Yao
Ann. Appl. Stat. 8(1): 622-647 (March 2014). DOI: 10.1214/13-AOAS711


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 max-stable 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.


Download Citation

Nicolas Raillard. Pierre Ailliot. Jianfeng Yao. "Modeling extreme values of processes observed at irregular time steps: Application to significant wave height." Ann. Appl. Stat. 8 (1) 622 - 647, March 2014.


Published: March 2014
First available in Project Euclid: 8 April 2014

zbMATH: 06302250
MathSciNet: MR3192005
Digital Object Identifier: 10.1214/13-AOAS711

Keywords: Composite likelihood , Extreme values , irregular time sampling , Max-stable process , satellite data , significant wave height , time series

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.8 • No. 1 • March 2014
Back to Top