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Nonlinear Granger Causality: Guidelines for Multivariate Analysis


  • Diks, C.G.H.

    () (University of Amsterdam)

  • Wolski, M.

    () (University of Amsterdam)


In this paper we propose an extension of the nonparametric Granger causality test, originally introduced by Diks and Panchenko [2006. A new statistic and practical guidelines for nonparametric Granger causality testing. Journal of Economic Dynamics \& Control 30, 1647-1669]. We show that the basic test statistics lacks consistency in the multivariate setting. The problem is the result of the kernel density estimator bias, which does not converge to zero at a sufficiently fast rate when the number of conditioning variables is larger than one. In order to overcome this difficulty we apply the data-sharpening method for bias reduction. We then derive the asymptotic properties of the `sharpened' test statistics and we investigate its performance numerically. We conclude with an empirical application to the US grain market.

Suggested Citation

  • Diks, C.G.H. & Wolski, M., 2013. "Nonlinear Granger Causality: Guidelines for Multivariate Analysis," CeNDEF Working Papers 13-15, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  • Handle: RePEc:ams:ndfwpp:13-15

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    1. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    2. Christopher L. Gilbert, 2010. "How to Understand High Food Prices," Journal of Agricultural Economics, Wiley Blackwell, vol. 61(2), pages 398-425, June.
    3. Sari, Ramazan & Hammoudeh, Shawkat & Chang, Chia-Lin & McAleer, Michael, 2012. "Causality between market liquidity and depth for energy and grains," Energy Economics, Elsevier, vol. 34(5), pages 1683-1692.
    4. Diks, Cees & Panchenko, Valentyn, 2006. "A new statistic and practical guidelines for nonparametric Granger causality testing," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1647-1669.
    5. Popp, Michael P. & Dillon, Carl R. & Keisling, Terry C., 2003. "Economic and weather influences on soybean planting strategies on heavy soils," Agricultural Systems, Elsevier, vol. 76(3), pages 969-984, June.
    6. Hiemstra, Craig & Jones, Jonathan D, 1994. "Testing for Linear and Nonlinear Granger Causality in the Stock Price-Volume Relation," Journal of Finance, American Finance Association, vol. 49(5), pages 1639-1664, December.
    7. 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.
    8. Peter Hall & Michael C. Minnotte, 2002. "High order data sharpening for density estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 141-157, January.
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