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A new test of multivariate nonlinear causality

Author

Listed:
  • Zhidong Bai
  • Yongchang Hui
  • Dandan Jiang
  • Zhihui Lv
  • Wing-Keung Wong
  • Shurong Zheng

Abstract

The multivariate nonlinear Granger causality developed by Bai et al. (2010) (Mathematics and Computers in simulation. 2010; 81: 5-17) plays an important role in detecting the dynamic interrelationships between two groups of variables. Following the idea of Hiemstra-Jones (HJ) test proposed by Hiemstra and Jones (1994) (Journal of Finance. 1994; 49(5): 1639-1664), they attempt to establish a central limit theorem (CLT) of their test statistic by applying the asymptotical property of multivariate U-statistic. However, Bai et al. (2016) (2016; arXiv: 1701.03992) revisit the HJ test and find that the test statistic given by HJ is NOT a function of U-statistics which implies that the CLT neither proposed by Hiemstra and Jones (1994) nor the one extended by Bai et al. (2010) is valid for statistical inference. In this paper, we re-estimate the probabilities and reestablish the CLT of the new test statistic. Numerical simulation shows that our new estimates are consistent and our new test performs decent size and power.

Suggested Citation

  • Zhidong Bai & Yongchang Hui & Dandan Jiang & Zhihui Lv & Wing-Keung Wong & Shurong Zheng, 2018. "A new test of multivariate nonlinear causality," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-14, January.
    • Handle: RePEc:plo:pone00:0185155
    DOI: 10.1371/journal.pone.0185155
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    References listed on IDEAS

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    1. Dufour, Jean-Marie & Pelletier, Denis & Renault, Eric, 2006. "Short run and long run causality in time series: inference," Journal of Econometrics, Elsevier, vol. 132(2), pages 337-362, June.
    2. Ghysels, Eric & Hill, Jonathan B. & Motegi, Kaiji, 2016. "Testing for Granger causality with mixed frequency data," Journal of Econometrics, Elsevier, vol. 192(1), pages 207-230.
    3. Jean-Marie Dufour & Eric Renault, 1998. "Short Run and Long Run Causality in Time Series: Theory," Econometrica, Econometric Society, vol. 66(5), pages 1099-1126, September.
    4. 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.
    5. 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.
    6. 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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    8. Jean-Marie Dufour & David Tessier, 2006. "Short-Run and Long-Run Causality between Monetary Policy Variables and Stock Prices," Staff Working Papers 06-39, Bank of Canada.
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