ROBUST OPTIMAL TESTS FOR CAUSALITY IN MULTIVARIATE TIME SERIES

Here, we derive optimal rank-based tests for noncausality in the sense of Granger between two multivariate time series+ Assuming that the global process admits a joint stationary vector autoregressive ~VAR! representation with an elliptically symmetric innovation density, both no feedback and one direction causality hypotheses are tested+ Using the characterization of noncausality in the VAR context, the local asymptotic normality ~LAN! theory described in Le Cam ~1986, Asymptotic Methods in Statistical Decision Theory! allows for constructing locally and asymptotically optimal tests for the null hypothesis of noncausality in one or both directions+ These tests are based on multivariate residual ranks and signs ~Hallin and Paindaveine, 2004a, Annals of Statistics 32, 2642–2678! and are shown to be asymptotically distribution free under elliptically symmetric innovation densities and invariant with respect to some affine transformations+ Local powers and asymptotic relative efficiencies are also derived+ The level, power, and robustness ~to outliers! of the resulting tests are studied by simulation and are compared to those of the Wald test+ Finally, the new tests are applied to Canadian money and income data+