This paper addresses the issue of over-rejection in nonparametric Granger causality tests, particularly the Hiemstra-Jones (HJ) test, and proposes a new test statistic to mitigate this problem. The authors develop asymptotic theory for the new test statistic and conduct a simulation study to compare its properties with the HJ test. The simulation results show that the new test maintains its size close to nominal and has high power, especially when the bandwidth tends to zero at an appropriate rate as the sample size increases. Transforming the time series to uniform marginals further improves the performance of both tests. The paper applies these tests to Standard and Poor's index volumes and returns, finding evidence of volume Granger-causing returns, but with weaker evidence after applying the recommended bandwidth adaptation and uniform transformation. The findings suggest that initial strong rejections may be spurious and that careful application of the proposed methods is necessary to avoid over-rejection.This paper addresses the issue of over-rejection in nonparametric Granger causality tests, particularly the Hiemstra-Jones (HJ) test, and proposes a new test statistic to mitigate this problem. The authors develop asymptotic theory for the new test statistic and conduct a simulation study to compare its properties with the HJ test. The simulation results show that the new test maintains its size close to nominal and has high power, especially when the bandwidth tends to zero at an appropriate rate as the sample size increases. Transforming the time series to uniform marginals further improves the performance of both tests. The paper applies these tests to Standard and Poor's index volumes and returns, finding evidence of volume Granger-causing returns, but with weaker evidence after applying the recommended bandwidth adaptation and uniform transformation. The findings suggest that initial strong rejections may be spurious and that careful application of the proposed methods is necessary to avoid over-rejection.