Nonparametric Tests for Conditional Independence Using Conditional Distributions

• Activity Number: 299
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Taoufik Bouezmarni* and Roch Roy+ and Abderrahim Taamouti
• Companies: McGill University and Université de Montréal and Universidad Carlos III de Madrid
• Keywords: Time series ; Granger causality ; Nadaraya-Watson estimator ; local bootstrap ; Asymptotic normality ; Finance applications

Abstract

The concept of causality is naturally defined in terms of conditional distributions, however almost all the empirical works in this literature focus on causality in mean. Here we propose a nonparametric statistic to test conditional independence and Granger non-causality between two random variables, conditionally on another one. The statistic is based on a quadratic distance between estimated conditional distribution functions using the Nadaraya-Watson method. We establish the asymptotic size and power properties of the new test and we motivate the validity of the local bootstrap. Its asymptotic power is better than that of Su and White (2008)'s test. We ran a simulation experiment to investigate its finite sample size properties and we illustrate its practical relevance by examining Granger non-causality between S&P 500 Index returns and many other financial variables.