A nonparametric bootstrap test for nonlinear Granger causality

An information theoretic test for Granger causality for stationary weakly dependent time series is proposed. The test statistic is based on conditional entropies. These quantities have nonparametric estimators which can be expressed in terms of correlation integrals. This provides a connection with the method proposed by Baek and Brock (1992), and its modified version developed by Hiemstra and Jones (1994). Several methodological issues are discussed, and some changes to the traditional approach proposed. The significance of the test statistic is determined using the stationary bootstrap by Politis and Romano (1994), rather than using an asymptotic normal approximation. The size and power of the bootstrap test are determined for various econometric time series models by Monte Carlo simulations. It is argued that bootstrapping only the hypothesized non-causing time series is to be preferred over bootstrapping both time series. It is shown that in the latter case the test becomes equivalent to a bootstrap version of the test for Granger causality developed by Hiemstra and Jones (1994), with the additional advantage that a simplified test statistic can be used.