Title: Noncausal heavy-tailed AR($p$) processes
Authors: Sebastien Fries - Hadamard PhD School in Mathematics (Paris-Saclay) and Crest (France) [presenting]
Jean-Michel Zakoian - CREST (France)
Abstract: The adjunction of a noncausal component to standard causal linear autoregressive processes often yields a better fit to economic and financial time series. The general framework of noncausal AR($p$) with possibly asymmetric $\alpha$-stable errors is investigated. The nonlinear causal dynamics is derived and shown to display quadratic GARCH effects in direct time. The existence of a unit root in this causal dynamics is of particular interest as it allows to exhibit linear noncausal processes which are stationary, and even positive, martingales. Finally, under the broader assumption that the errors belong to the domain of attraction of a stable distribution, it is shown that contrary to the OLS estimator, the LAD estimator of the autoregressive parameters is able to identify causal and noncausal structures.