Nonparametric tests for conditional independence using conditional distributions

Bouezmarni, T.; Taamouti, A.

doi:10.1080/10485252.2014.945447

Nonparametric tests for conditional independence using conditional distributions

Bouezmarni, T.; Taamouti, A.

Authors

T. Bouezmarni

Professor Abderrahim Taamouti abderrahim.taamouti@durham.ac.uk
Visiting Fellow

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

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Copyright Statement
This is an Accepted Manuscript of an article published by Taylor & Francis Group in Journal of Nonparametric Statistics on 15/08/2014, available online at: http://www.tandfonline.com/10.1080/10485252.2014.945447.