This paper introduces a new test statistic for nonparametric Granger causality testing, addressing issues of size distortion in the Hiemstra-Jones (HJ) test. The authors demonstrate that the HJ test can suffer from over-rejection when the bandwidth is too large, especially in the presence of conditional heteroskedasticity. They propose a modified test statistic, $ T_n $, which is based on a U-statistic and avoids this bias. The new test is shown to maintain good size properties when the bandwidth is chosen appropriately, and its power remains high. The paper also shows that transforming the data to uniform marginals can improve the performance of both tests. Simulation studies indicate that the new test performs well compared to the HJ test, particularly when the bandwidth is adapted to the sample size. In an application to Standard and Poor's index data, the HJ test suggests that volume Granger-causes returns, but this evidence weakens when the simulation-based recommendations are applied. The paper concludes that the new test provides a more reliable method for testing Granger causality in financial time series.This paper introduces a new test statistic for nonparametric Granger causality testing, addressing issues of size distortion in the Hiemstra-Jones (HJ) test. The authors demonstrate that the HJ test can suffer from over-rejection when the bandwidth is too large, especially in the presence of conditional heteroskedasticity. They propose a modified test statistic, $ T_n $, which is based on a U-statistic and avoids this bias. The new test is shown to maintain good size properties when the bandwidth is chosen appropriately, and its power remains high. The paper also shows that transforming the data to uniform marginals can improve the performance of both tests. Simulation studies indicate that the new test performs well compared to the HJ test, particularly when the bandwidth is adapted to the sample size. In an application to Standard and Poor's index data, the HJ test suggests that volume Granger-causes returns, but this evidence weakens when the simulation-based recommendations are applied. The paper concludes that the new test provides a more reliable method for testing Granger causality in financial time series.