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Robust Optimal Tests For Causality In Multivariate Time Series

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  • Saidi, Abdessamad
  • Roy, Roch

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.

Suggested Citation

  • Saidi, Abdessamad & Roy, Roch, 2008. "Robust Optimal Tests For Causality In Multivariate Time Series," Econometric Theory, Cambridge University Press, vol. 24(4), pages 948-987, August.
  • Handle: RePEc:cup:etheor:v:24:y:2008:i:04:p:948-987_08
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    Cited by:

    1. Taoufik Bouezmarni & Abderrahim Taamouti, 2014. "Nonparametric tests for conditional independence using conditional distributions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(4), pages 697-719, December.
    2. Bauer, Dietmar & Maynard, Alex, 2012. "Persistence-robust surplus-lag Granger causality testing," Journal of Econometrics, Elsevier, vol. 169(2), pages 293-300.
    3. Dietmar Bauer & Alex Maynard, 2010. "Persistence-robust Granger causality testing," Working Papers 1011, University of Guelph, Department of Economics and Finance.
    4. Ruiz-Castillo, Javier, 2012. "From the “European Paradox” to a European Drama in citation impact," UC3M Working papers. Economics we1211, Universidad Carlos III de Madrid. Departamento de Economía.
    5. Bai, Zhidong & Wong, Wing-Keung & Zhang, Bingzhi, 2010. "Multivariate linear and nonlinear causality tests," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 5-17.

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