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Nonparametric tests for conditional independence using conditional distributions

  • Taamouti, Abderrahim
  • Bouezmarni, Taoufik

The concept of causality is naturally defined in terms of conditional distribution, however almost all the empirical works focus on causality in mean. This paper aim to propose a nonparametric statistic to test the conditional independence and Granger non-causality between two variables conditionally on another one. The test statistic is based on the comparison of conditional distribution functions using an L2 metric. We use Nadaraya-Watson method to estimate the conditional distribution functions. We establish the asymptotic size and power properties of the test statistic and we motivate the validity of the local bootstrap. Further, we ran a simulation experiment to investigate the finite sample properties of the test and we illustrate its practical relevance by examining the Granger non-causality between S&P 500 Index returns and VIX volatility index. Contrary to the conventional t-test, which is based on a linear mean-regression model, we find that VIX index predicts excess returns both at short and long horizons.

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Paper provided by Universidad Carlos III de Madrid. Departamento de Economía in its series UC3M Working papers. Economics with number we1217.

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Date of creation: 06 Jan 2012
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Handle: RePEc:cte:werepe:we1217
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  1. Taamouti, Abderrahim & Dufour, Jean-Marie, 2008. "Short and long run causality measures: theory and inference," UC3M Working papers. Economics we083720, Universidad Carlos III de Madrid. Departamento de Economía.
  2. Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, vol. 18(01), pages 169-192, February.
  3. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
  4. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355, 01-2013.
  5. Pierce, David A. & Haugh, Larry D., 1977. "Causality in temporal systems : Characterization and a survey," Journal of Econometrics, Elsevier, vol. 5(3), pages 265-293, May.
  6. Fan, Yanqin & Li, Qi, 2000. "Consistent Model Specification Tests," Econometric Theory, Cambridge University Press, vol. 16(06), pages 1016-1041, December.
  7. Ait-Sahalia, Yacine & Bickel, Peter J. & Stoker, Thomas M., 2001. "Goodness-of-fit tests for kernel regression with an application to option implied volatilities," Journal of Econometrics, Elsevier, vol. 105(2), pages 363-412, December.
  8. Gourieroux,Christian & Monfort,Alain, 1997. "Time Series and Dynamic Models," Cambridge Books, Cambridge University Press, number 9780521411462, September.
  9. Meitz, Mika & Saikkonen, Pentti, 2004. "Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models," SSE/EFI Working Paper Series in Economics and Finance 573, Stockholm School of Economics, revised 20 Apr 2007.
  10. Saidi, Abdessamad & Roy, Roch, 2008. "Robust Optimal Tests For Causality In Multivariate Time Series," Econometric Theory, Cambridge University Press, vol. 24(04), pages 948-987, August.
  11. Su, Liangjun & White, Halbert, 2008. "A Nonparametric Hellinger Metric Test For Conditional Independence," Econometric Theory, Cambridge University Press, vol. 24(04), pages 829-864, August.
  12. P. M. Robinson, 1991. "Consistent Nonparametric Entropy-Based Testing," Review of Economic Studies, Oxford University Press, vol. 58(3), pages 437-453.
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