Nonparametric tests for conditional independence using conditional distributions

Taoufik Bouezmarni
Authors registered in the RePEc Author Service: Abderrahim Taamouti

UC3M Working papers. Economics from Universidad Carlos III de Madrid. Departamento de Economía

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 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.

Keywords: Nonparametric; tests; Time; series; Conditional; independence; Granger; non-causality; Nadaraya-Watson; estimator; Conditional; distribution; function; VIX; volatility; index; S&P500; index (search for similar items in EconPapers)
JEL-codes: C12 C14 C15 C19 E3 E4 G1 G12 (search for similar items in EconPapers)
Date: 2012-01-06
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (1)

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