A0473
Title: Deconvolution and filtering of non-causal alpha-stable processes
Authors: Ludivine Vaudree - University of Orleans (France) [presenting]
Gilles De Truchis - University of Orleans (France)
Arthur Thomas - Paris Dauphine University - PSL (France)
Abstract: The purpose is to develop a comprehensive theoretical framework for the deconvolution and filtering of time series processes composed of aggregated non-causal alpha-stable AR(1) components. Rigorous identification conditions are established based on the characteristic function, and efficient sequential estimation methods are proposed. The approach allows for the modeling of multiple local explosive behaviors occurring at different rates, such as those observed in financial time series exhibiting speculative bubbles. Upon establishing parameter identification, a particle filtering method is introduced based on Markov chain Monte Carlo techniques, specifically designed for the recovery of latent components in alpha-stable mixture models. This filtering methodology effectively addresses the challenges inherent to alpha-stable distributions, including heavy tails and the lack of closed-form densities. The framework is developed for both continuous and discrete domains. This combination of parameter estimation and filtering techniques enables the analysis of financial time series exhibiting locally explosive patterns while preserving stationarity.
