A0451
Title: Forecasting extreme trajectories using semi-norm representations
Authors: Gilles De Truchis - University of Orleans (France)
Sebastien Fries - Vrije Universiteit Amsterdam (Netherlands)
Arthur Thomas - Paris Dauphine University - PSL (France) [presenting]
Abstract: For a two-sided stable moving average, the conditional distribution of future paths is studied, given a piece of observed trajectory when the process is far from its central values. Under this framework, vectors of the form $Xt =(Xt-m, . . . ,Xt, Xt+1, . . . ,Xt+h)$, $m >0$, $h>1$, are multivariate stable, and the dependence between the past and future components is encoded in their spectral measures. A new representation of stable random vectors on unit cylinder sets for an adequate semi-norm is proposed to describe the tail behaviour of vectors Xt when only the first m+1 components are assumed to be observed and large in norm. Not all stable vectors admit such a representation, and (Xt) must be anticipative enough for Xt to admit one. The conditional distribution of future paths can then be explicitly derived using the regularly varying tails property of stable vectors, which has a natural interpretation in terms of pattern identification. Through Monte Carlo simulations, procedures are developed to forecast crash probabilities and crash dates and demonstrate their finite sample performances. Probabilities and reversal dates of El Nio and La Nia occurrences are estimated as an empirical illustration.
