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ROBUST OPTIMAL TESTS FOR CAUSALITY IN MULTIVARIATE TIME SERIES

Published online by Cambridge University Press:  04 April 2008

Abdessamad Saidi  and
Roch Roy
Abdessamad Saidi
Affiliation:
Université de Montréal
Roch Roy*
Affiliation:
Université de Montréal
*
Address correspondence to Roch Roy, Département de mathématiques et de statistique, Université de Montréal, CP 6128, succursale Centre-ville, Montréal, Québec, H3C 3J7, Canada; e-mail: royr@dms.umontreal.ca.
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Abstract

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.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 4 , August 2008 , pp. 948 - 987
Copyright
Copyright © Cambridge University Press 2008

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