A0404
Title: Multivariate seminorm representation for alpha-stable moving average processes and path prediction
Authors: Gilles De Truchis - University of Orléans (France) [presenting]
Arthur Thomas - Paris Dauphine University - PSL (France)
Sebastien Fries - Vrije Universiteit Amsterdam (Netherlands)
Abstract: For a univariate process X(t) modeled as a two-sided alpha-stable moving average, the dependence between the past and future components of vectors of the form (X(t-m), ..., X(t), X(t+1), ..., X(t+h)), where m >= 0 and h >= 1, is encoded in their spectral measures. This dependence can be represented on unit cylinder sets for an appropriate seminorm only if the process is "anticipative enough." This framework allows for the explicit derivation of the conditional distribution of future paths when only the first m+1 components are observed and large in norm. From this, one can deduce a forecasting procedure capable of determining the crash date of an extreme event if the underlying univariate process is noncausal. This representation is extended to general multivariate alpha-stable moving averages, where new properties emerge in higher dimensions, where, in particular, the presence of a non-anticipative component does not rule out the existence of adequate seminorm representations. This leads to an interesting result: Extreme events (peak and crash dates) of purely causal processes (which are otherwise unpredictable) can be inferred from a noncausal variable estimated within the same multivariate system, as they are linked by the error term. This serves as proof of early warning. For practical applications, a closed-form expression is proposed for the conditional distribution of future paths in an alpha-stable mixed causal VAR model.
