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Nonparametric tests for conditional independence using conditional distributions

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  • 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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    Cited by:

    1. Taoufik Bouezmarni & Mohamed Doukali & Abderrahim Taamouti, 2023. "Testing Granger Non-Causality in Expectiles," University of East Anglia School of Economics Working Paper Series 2023-02, School of Economics, University of East Anglia, Norwich, UK..
    2. Su, Liangjun & White, Halbert, 2014. "Testing conditional independence via empirical likelihood," Journal of Econometrics, Elsevier, vol. 182(1), pages 27-44.
    3. Taoufik Bouezmarni & Mohamed Doukali & Abderrahim Taamouti, 2022. "Testing Granger Non-Causality in Expectiles," Working Papers 202207, University of Liverpool, Department of Economics.
    4. 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.

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    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • G1 - Financial Economics - - General Financial Markets
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
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    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
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