A Nonparametric Test For Instantaneous Causality With Time-Varying Variances

This paper proposes a consistent nonparametric test with good sampling properties to detect instantaneous causality between vector autoregressive (VAR) variables with time-varying variances. The new test takes the form of the U-statistic, and has a limiting standard normal distribution under the null. We further show that the test is consistent against any fixed alternatives, and has nontrivial asymptotic power against a class of local alternatives with a rate slower than $T^{-1/2}$ . We also propose a wild bootstrap procedure to better approximate the finite sample null distribution of the test statistic. Monte Carlo experiments are conducted to highlight the merits of the proposed test relative to other popular tests in finite samples. Finally, we apply the new test to investigate the instantaneous causality relationship between money supply and inflation rates in the USA.