Title: Elliptical subset VAR estimation and impacts on frequency causality measures
Authors: Thibault Soler - University Paris 1 -- Pantheon-Sorbonne (France) [presenting]
Emmanuelle Jay - Fideas Capital (France)
Christophe Chorro - University (France)
Philippe De Peretti - Pantheon-Sorbonne University - Paris 1 (France)
Abstract: Granger non-causality tests have received a great deal of attention over recent years, especially in economics, finance and neuroscience. Nevertheless, they report no information about the causal strength, which is often required. To correct this aspect, several measures in frequency domain has been proposed. These approaches are two-step ones consisting in first estimating a Vector AutoRegressive model (VAR), and then computing coherence of transfer function. While being very appealing, this two-stages procedure may suffer from an inaccurate estimation of the VAR coefficients, in particular for heavy-tailed time series, short sample size, or highly correlated innovations. We propose to focus on heavy-tailed estimation, which is more appropriate to modelling economic or financial time series, and our goal is twofold: first, extend Gaussian subset VAR estimation to elliptical using robust covariance matrix. Then, evaluate the impact on generalized partial directed coherence. The method uses Tyler's covariance matrix estimator and Yule-Walker equations to estimate VAR coefficients, which allows to reduce the estimation error of the coefficients due to extreme values. The empirical performance is demonstrated using Monte-Carlo simulations with different kind of multivariate systems and innovation assumptions (distribution, covariance structure, etc.), and the results obtained are then compared with those of other covariance matrix estimators (SCM, $Q_n$ estimator, etc.).