Modified Hiemstra-Jones Test for Granger Non-causality

The paper addresses a problem in a frequently used nonparametric test for Granger causality (Hiemstra and Jones, 1994). Some examples suffice to show that the equality tested in general is not an implication of the null hypothesis of conditional independence. Upon deriving the asymptotic bias we indeed find that the commonly used test procedure leads to inconsistencies. Monte Carlo simulations using certain processes satisfying the null hypothesis show that, for a given nominal size, the actual rejection rate may tend to one as the sample size increases. Motivated by these results we propose an alternative test statistic and develop its asymptotic distribution theory. Monte Carlo simulations show that the actual size of the new test is closer to nominal, particularly in the presence of conditional heteroskedasticity. Our results offer (at least partial) explanations for several anomalies reported in the applied empirical literature, notably those suggesting strong evidence for trading volume Granger-causing returns. For daily S&P500 returns and trading volume data, our approach suggests that the evidence is in fact weaker than suggested by the Hiemstra-Jones test.