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

• Published in: The Annals of Applied Statistics
• Main Authors: Raillard, Nicolas, Ailliot, Pierre, Yao, Jian-Feng
• Other Authors: Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Laboratoire de Mathématiques de Bretagne Atlantique (LMBA), Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS), Department of Statistics and Actuarial Science University of Hong Kong (DSAS), The University of Hong Kong (HKU)
• Format: Article in Journal/Newspaper
• Language: English
• Published: HAL CCSD 2014
• Subjects: Extreme values; time series; max-stable process; composite likelihood; consistency; irregular time sampling; significant wave height; altimeter; [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]; [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH]; North Atlantic
• Online Access: https://hal.science/hal-00656473; https://hal.science/hal-00656473v2/document; https://hal.science/hal-00656473v2/file/article.pdf; https://doi.org/10.1214/13-AOAS711

26 pages International audience 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 datasets 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.