A0798
Title: Local stationarity in the extremes
Authors: Manon Felix - University of Geneva (Switzerland) [presenting]
Davide La Vecchia - University of Geneva (Switzerland)
Gilles Stupfler - University of Angers (France)
Abstract: The purpose is to present a novel approach that bridges extreme theory and non-stationary theory, aiming to characterize the concept of E-local stationarity. Unlike conventional literature on locally stationary processes, the proximity between a non-stationary process and its stationary approximation cannot be defined solely in terms of the Lp norm due to the potential non-existence of the first moment. Consequently, the methodology relies on pre-asymptotic measures. By leveraging extreme theory applicable to strictly stationary and strongly mixing (potentially multivariate) processes, we develop a localized extremogram in time. Conditions are established to ensure the asymptotic normality of the empirical extremogram, which is weighted by a kernel and centered by a pre-asymptotic version. Furthermore, the properties of the frequency domain analog of the extremogram are derived within the framework.
