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Nonparametric tests for conditional independence using conditional distributions

Author

Listed:
  • Taoufik Bouezmarni
  • Abderrahim Taamouti

Abstract

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 aims 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 L 2 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. 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, we find that VIX index predicts excess returns both at short and long horizons.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:gnstxx:v:26:y:2014:i:4:p:697-719
    DOI: 10.1080/10485252.2014.945447
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    References listed on IDEAS

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    1. Meitz, Mika & Saikkonen, Pentti, 2008. "Ergodicity, Mixing, And Existence Of Moments Of A Class Of Markov Models With Applications To Garch And Acd Models," Econometric Theory, Cambridge University Press, vol. 24(05), pages 1291-1320, October.
    2. Gourieroux,Christian & Monfort,Alain, 1997. "Time Series and Dynamic Models," Cambridge Books, Cambridge University Press, number 9780521423083, March.
    3. P. M. Robinson, 1991. "Consistent Nonparametric Entropy-Based Testing," Review of Economic Studies, Oxford University Press, vol. 58(3), pages 437-453.
    4. 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.
    5. Dufour, Jean-Marie & Taamouti, Abderrahim, 2010. "Short and long run causality measures: Theory and inference," Journal of Econometrics, Elsevier, vol. 154(1), pages 42-58, January.
    6. 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.
    7. Granger, C. W. J. & Newbold, Paul, 1986. "Forecasting Economic Time Series," Elsevier Monographs, Elsevier, edition 2, number 9780122951831 edited by Shell, Karl.
    8. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    9. Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, vol. 18(01), pages 169-192, February.
    10. Fan, Yanqin & Li, Qi, 2000. "Consistent Model Specification Tests," Econometric Theory, Cambridge University Press, vol. 16(06), pages 1016-1041, December.
    11. 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.
    12. 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.
    13. 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.
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    Cited by:

    1. Su, Liangjun & White, Halbert, 2014. "Testing conditional independence via empirical likelihood," Journal of Econometrics, Elsevier, vol. 182(1), pages 27-44.
    2. repec:bpj:sndecm:v:21:y:2017:i:4:p:20:n:3 is not listed on IDEAS
    3. Gonzalo Jesús & Taamouti Abderrahim, 2017. "The reaction of stock market returns to unemployment," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(4), pages 1-20, September.

    More about this item

    JEL classification:

    • E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates
    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G1 - Financial Economics - - General Financial Markets
    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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