Nonparametric tests for conditional independence using conditional distributions

Bouezmarni, T.; Taamouti, A.

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 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. 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.

Citation

Bouezmarni, T., & Taamouti, A. (2014). Nonparametric tests for conditional independence using conditional distributions. Journal of Nonparametric Statistics, 26(4), 697-719. https://doi.org/10.1080/10485252.2014.945447

• Journal Article Type: Article
• Acceptance Date: Jul 8, 2014
• Online Publication Date: Aug 15, 2014
• Publication Date: Oct 2, 2014
• Deposit Date: Oct 16, 2014
• Publicly Available Date: Mar 3, 2015
• Journal: Journal of Nonparametric Statistics
• Print ISSN: 1048-5252
• Electronic ISSN: 1029-0311
• Publisher: Taylor and Francis Group
• Peer Reviewed: Peer Reviewed
• Volume: 26
• Issue: 4
• Pages: 697-719
• DOI: https://doi.org/10.1080/10485252.2014.945447
• Keywords: Nonparametric tests, Time series, Conditional independence, Granger non-causality, Nadaraya–Watson estimator, Conditional distribution function, VIX volatility index, S&P500 Index.
• Public URL: https://durham-repository.worktribe.com/output/1421834