Causality in Quantiles and Dynamic Stock Return-Volume Relations

This paper investigates the causal relations between stock return and volume based on quantile regressions. We first define Granger non-causality in all quantiles and propose testing non-causality by a sup-Wald test. Such a test is consistent against any deviation from non-causality in distribution, as opposed to the existing tests that check only noncausality in certain moment. This test is readily extended to test non-causality in different quantile ranges, and the testing results enable us to identify the quantile range for which causality is relevant. In the empirical studies of 3 major stock market indices, we find that, while the conventional test suggests no causality in mean, there are strong evidences that lagged volume Granger causes return in all but some middle quantiles. In particular, the causal effects have opposite signs at lower and upper quantiles and are stronger at more extreme quantiles. These relations form (symmetric) V shapes across quantiles. They also show that the dispersion of the return distribution increases with volume so that volume has a positive effect on return volatility. It is also shown that the quantile causal effects of lagged return on volume are mainly negative.