A0551
Title: Asymptotic theory for the likelihood-based block maxima method in time series
Authors: Simone Padoan - Bocconi University (Italy) [presenting]
David Carl - Bocconi University (Italy)
Stefano Rizzelli - University of Padova (Italy)
Abstract: An asymptotic framework is developed for likelihood-based inference in the block maxima (BM) method for stationary time series. While Bayesian inference under the BM approach has been widely studied in the independence setting, no asymptotic theory currently exists for time series. Further results are needed to establish that the BM method can be applied with the kind of dependent time series models relevant to applied fields. To address this gap, a comprehensive likelihood theory is first established for the misspecified generalized extreme value (GEV) model under serial dependence. Building on this foundation, the asymptotic theory of Bayesian inference is developed for the GEV parameters, the extremal index, $T$-time-horizon return levels, and extreme quantiles (value at risk). For inference on the extremal index, an adjusted posterior distribution is proposed that corrects for poor coverage exhibited by a naive Bayesian approach. Simulations show excellent inferential performances for the proposed methodology.
