|Institution:||Université Catholique de Louvain|
|Keywords:||Statistics of extremes; Spectral measure; Regular variation; Stationary time series; Heavy-tailed Markov chains; Heavy-tailed time series|
|Full text PDF:||http://hdl.handle.net/2078.1/176771|
There is an increasing interest to understand the interplay of extreme values over time and across coordinates. Extreme-value theory provides techniques for modeling temporal and cross-sectional extremal dependence by modeling the marginal distributions and the dependence structure separately. Regular variation is the key assumption in this context. Inference about serial extremal dependence within a time series can be made via the spectral tail process. For estimating dependence at high levels within a multivariate random vector, the spectral measure is particularly convenient. The aim of this thesis is to extend the statistical toolbox for modeling extremal dependence in space or time. In particular, the focus is on nonparametric techniques for estimating the spectral tail process and the spectral measure. Appropriate estimators are constructed and their large-sample distribution is derived. Their finite-sample performance is evaluated via Monte Carlo simulations. Throughout the theory is illustrated on financial or weather data. (SC - Sciences) – UCL, 2016 Advisors/Committee Members: UCL - SSH/IMAQ/ISBA - Institut de Statistique, Biostatistique et Sciences Actuarielles, UCL - Faculté des Sciences, Devolder, Pierre, Davis, Richard, Drees, Holger, Johannes, Jan, von Sachs, Rainer, Veredas, David, Segers, Johan.