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A NONPARAMETRIC HELLINGER METRIC TEST FOR CONDITIONAL INDEPENDENCE

Published online by Cambridge University Press:  04 April 2008

Liangjun Su  and
Halbert White
Liangjun Su
Affiliation:
Singapore Management University
Halbert White*
Affiliation:
University of California, San Diego
*
Address correspondence to Halbert White, Department of Economics, University of California, San Diego, La Jolla, CA 92093-0508, USA; e-mail: hwhite@econ.ucsd.edu.
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Abstract

We propose a nonparametric test of conditional independence based on the weighted Hellinger distance between the two conditional densities, f(y|x,z) and f(y|x), which is identically zero under the null. We use the functional delta method to expand the test statistic around the population value and establish asymptotic normality under β-mixing conditions. We show that the test is consistent and has power against alternatives at distance n−1/2h−d/4. The cases for which not all random variables of interest are continuously valued or observable are also discussed. Monte Carlo simulation results indicate that the test behaves reasonably well in finite samples and significantly outperforms some earlier tests for a variety of data generating processes. We apply our procedure to test for Granger noncausality in exchange rates.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 4 , August 2008 , pp. 829 - 864
Copyright
Copyright © Cambridge University Press 2008

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