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A nonparametric copula based test for conditional independence with applications to Granger causality

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  • BOUEZMARNI, Taoufik
  • ROMBOUTS, Jeroen

    ()
    (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE))

  • TAAMOUTI, Abderrahim

Abstract

This paper proposes a new nonparametric test for conditional independence, which is based on the comparison of Bernstein copula densities using the Hellinger distance. The test is easy to implement because it does not involve a weighting function in the test statistic, and it can be applied in general settings since there is no restriction on the dimension of the data. In fact, to apply the test, only a bandwidth is needed for the nonparametric copula. We prove that the test statistic is asymptotically pivotal under the null hypothesis, establish local power properties, and motivate the validity of the bootstrap technique that we use in finite sample settings. A simulation study illustrates the good size and power properties of the test. We illustrate the empirical relevance of our test by focusing on Granger causality using financial time series data to test for nonlinear leverage versus volatility feedback effects and to test for causality between stock returns and trading volume. In a third application, we investigate Granger causality between macroeconomic variables. Le présent document propose un nouveau test non paramétrique d’indépendance conditionnelle, lequel est fondé sur la comparaison des densités de la copule de Bernstein suivant la distance de Hellinger. Le test est facile à réaliser, du fait qu’il n’implique pas de fonction de pondération dans les variables utilisées et peut être appliqué dans des conditions générales puisqu’il n’y a pas de restriction sur l’étendue des données. En fait, dans le cas de la copule non paramétrique, l’application du test ne requiert qu’une largeur de bande. Nous démontrons que les variables utilisées pour le test jouent asymptotiquement un rôle crucial sous l’hypothèse nulle. Nous établissons aussi les propriétés des pouvoirs locaux et justifions la validité de la technique bootstrap (technique d’auto-amorçage) que nous utilisons dans les contextes où les échantillons sont d

(This abstract was borrowed from another version of this item.)

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2009041.

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Date of creation: 01 Jun 2009
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Handle: RePEc:cor:louvco:2009041

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Keywords: nonparametric tests; conditional independence; Granger non-causality; Bernstein density copula; bootstrap; finance; volatility asymmetry; leverage effect; volatility feedback effect; macroeconomics;

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Cited by:
  1. Jesús Gonzalo & AbderrahimTaamouti, 2012. "The reaction of stock market returns to anticipated unemployment," Economics Working Papers we1237, Universidad Carlos III, Departamento de Economía.

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