Abstract
This article introduces a kernel-based nonparametric inferential procedure to test for Granger causality in distribution. This test is a multivariate extension of the kernel-based Granger causality test in tail event. The main advantage of this test is its ability to examine a large number of lags, with higher-order lags discounted. In addition, our test is highly flexible because it can be used to identify Granger causality in specific regions on the distribution supports, such as the center or tails. We prove that the test converges asymptotically to a standard Gaussian distribution under the null hypothesis and thus is free of parameter estimation uncertainty. Monte Carlo simulations illustrate the excellent small sample size and power properties of the test. This new test is applied to a set of European stock markets to analyze spillovers during the recent European crisis and to distinguish contagion from interdependence effects.
Highlights
Analysis of causal relationships holds an important part of the theoretical and empirical contributions in quantitative economics (See the special issues of the Journal of Econometrics in 1988 and 2006)
Our test statistic is a multivariate extension of the kernel-based nonparametric Granger-causality test in tail-event by Hong et al (2009), and shares its main advantage: it checks for a large number of lags by discounting higher order lags
We show that the test has a standard Gaussian distribution under the null hypothesis which is free of parameter estimation uncertainty
Summary
Analysis of causal relationships holds an important part of the theoretical and empirical contributions in quantitative economics (See the special issues of the Journal of Econometrics in 1988 and 2006). The test can be used to test for causality in the left-tail distribution for two time series In this case the multivariate process of inter-quantile event variables should be defined so as to focus the analysis exclusively on this part of the distribution. Our test statistic is a multivariate extension of the kernel-based nonparametric Granger-causality test in tail-event by Hong et al (2009), and shares its main advantage: it checks for a large number of lags by discounting higher order lags This characteristic is consistent with the stylized fact in empirical finance that recent events have much more influence in the current market trends than those older.
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