## The Annals of Applied Statistics

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

#### Abstract

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.

#### Article information

Source
Ann. Appl. Stat., Volume 8, Number 1 (2014), 622-647.

Dates
First available in Project Euclid: 8 April 2014

https://projecteuclid.org/euclid.aoas/1396966301

Digital Object Identifier
doi:10.1214/13-AOAS711

Mathematical Reviews number (MathSciNet)
MR3192005

Zentralblatt MATH identifier
06302250

#### Citation

Raillard, Nicolas; Ailliot, Pierre; Yao, Jianfeng. Modeling extreme values of processes observed at irregular time steps: Application to significant wave height. Ann. Appl. Stat. 8 (2014), no. 1, 622--647. doi:10.1214/13-AOAS711. https://projecteuclid.org/euclid.aoas/1396966301

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#### Supplemental materials

• Supplementary material: Supplementary material: Proof of the consistency of the MPL1E estimates. In the attached supplemental material [Raillard, Ailliot and Yao (2013)], we prove the consistency of the $\mathrm{MPL}_{1}\mathrm{E}$ estimator in an idealized situation with no censoring and known marginal distributions.