Nonparametric estimation and inference for conditional density based Granger causality measures

Abstract

Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Journal of Econometrics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be re ected in this document. Changes may have been made to this work since it was submitted for publication. A de nitive version was subsequently published in Journal of Econometrics, 180, 2, June 2014, 10.1016/j.jeconom.2014.03.001. Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. ABSTRACTWe propose a nonparametric estimation and inference for conditional density based Granger causality measures that quantify linear and nonlinear Granger causalities. We first show how to write the causality measures in terms of copula densities. Thereafter, we suggest consistent estimators for these measures based on a consistent nonparametric estimator of copula densities. Furthermore, we establish the asymptotic normality of these nonparametric estimators and discuss the validity of a local smoothed bootstrap that we use in finite sample settings to compute a bootstrap bias-corrected estimator and to perform statistical tests. A Monte Carlo simulation study reveals that the bootstrap bias-corrected estimator behaves well and the corresponding test has quite good finite sample size and power properties for a variety of typical data generating processes and different sample sizes. Finally, two empirical applications are considered to illustrate the practical relevance of nonparametric causality measures.JEL Classification: C12; C14; C15; C19; G1; G12; E3; E4.

Causality in distribution between European stock markets and commodity prices: using independence test based on the empirical copula

“…Second, a copula function can be used for Granger causality analysis and information transmission (usually volatility transmission). To the best of our knowledge, there are only several studies in this field, for example: [Lee, Yang 2014;Bouezmarni, Rombouts, Taamouti 2012;Taamouti, Bouezmarni, El Ghouch 2014], but none of them deals with the relations between commodity prices and stock markets.…”

A Nonparametric Test for Granger Causality in Distribution With Application to Financial Contagion

“…Testing procedures for Granger causality in the whole distribution in a time series context are developed only in Su and White (2007, Bouezmarni, Rombouts, and Taamouti (2012), and Taamouti, Bouezmarni, and El Ghouch (2014). For example, Su and White (2012) introduced a conditional independence specification test that can be used to test for Granger causality in quantiles over a continuum of values of quantile levels between (0, 1).…”

“…Bouezmarni, Rombouts, and Taamouti (2012) constructed a nonparametric Granger causality test in distribution based on conditional independence in the framework of copulas. Taamouti, Bouezmarni, and El Ghouch (2014) also developed alternative Granger causality tests using the copulas theory. The present article adds to this literature by proposing a new nonparametric test for Granger causality in the whole distribution between two time series.…”

“…In this case, the multivariate process of interquantile event variables should be defined to focus the analysis exclusively on this part of the distribution. This flexibility constitutes a clear advantage of our methodology compared to those based on copulas theory (Bouezmarni, Rombouts, and Taamouti 2012;Taamouti, Bouezmarni, and El Ghouch 2014) and allows us to go beyond the simple rejection of the null hypothesis of Granger causality for the whole distribution because it identifies the specific regions for which Granger causality is rejected. Our test statistic is also a multivariate extension of the kernel-based nonparametric Granger causality test in tail events by Hong, Liu, and Wang (2009) and therefore shares its main advantage: the ability to examine a large number of lags by discounting higher-order lags.…”

Measuring Nonlinear Granger Causality in Mean

“…Polasek (1994Polasek ( , 2002 show how causality measures can be computed using Akaike Information Criterion (AIC) and a Bayesian approach. Taamouti et al (2014) have recently proposed a nonparametric estimator and test for Granger causality measures that quantify Granger causality in distribution. However, the main issue of Taamouti et al's (2014) measures is that they are not informative about the level(s) (mean, variance, other high-order moments, quantiles) of distribution where the causality exists.…”