Testing Conditional Independence Via Empirical Likelihood
AbstractLet f(y|x,z) (resp. f(y|x) be the conditional density of Y given (X,Z) (resp. X). We construct a class of `smoothed` empirical likelihood-based tests for the conditional independence hypothesis: Pr[f(Y|X,Z)=f(Y|X)]=1. We show that the test statistics are asymptotically normal under the null hypothesis and derive their asymptotic distributions under a sequence of local alternatives. The tests are shown to possess a weak optimality property in large samples. Simulation results suggest that the tests behave well in finite samples. Applications to some economic and financial time series indicate that our tests reveal some interesting nonlinear causal relations which the traditional linear Granger causality test fails to detect.
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Bibliographic InfoPaper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number qt35v8g0fm.
Date of creation: 01 Oct 2003
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Conditional Independence; b-mixing;
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- Taoufik Bouezmarni & Jeroen Rombouts & Abderrahim Taamouti, 2009.
"A Nonparametric Copula Based Test for Conditional Independence with Applications to Granger Causality,"
CIRANO Working Papers
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- Yoon-Jae Whang, 2004. "Smoothed Empirical Likelihood Methods for Quantile Regression Models," Cowles Foundation Discussion Papers 1453, Cowles Foundation for Research in Economics, Yale University.
- Kyungchul Song, 2007. "Testing Conditional Independence via Rosenblatt Transforms," PIER Working Paper Archive 07-026, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
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