Center for Advanced Intelligence Project

Title: Path prediction of aggregated α-stable moving averages using semi-norm representations

Abstract:
For (Xt) a two-sided α-stable moving average, this paper studies the conditional distribution of future paths 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 α-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 cylinders –sets {s∈Rm+h+1: ‖s‖= 1} for ‖·‖ an adequate semi-norm– is proposed in order 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) will have to 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 and has a natural interpretation in terms of pattern identification. The approach extends to processes resulting from the linear combination of stable moving averages which feature much richer dynamics and applied to several examples.

Bio:
Sébastien Fries is a tenure-track Assistant Professor at the Department of Econometrics and Data Science of the Vrije Universiteit Amsterdam, and a Marie Skłodowska-Curie Fellow. He holds an Engineer’s degree from ENSAE Paris, a M.Sc. in Economics from Paris School of Economics and he completed a PhD in Mathematics at Paris-Saclay University in 2018 focusing on the probabilistic prediction theory of so-called anticipative, or noncausal, heavy-tailed processes which remains his main research line. He teaches applied and theoretical machine learning at bachelor and master level.