New Evidence on the Relation between Return Volatility and Trading Volume

In his seminal paper, Brooks argues that the relation between return volatility and trading volume can be both linear and nonlinear. Adopting both linear and nonlinear Granger causality tests, he shows that there exists both linear and nonlinear bi-directional causality between trading volumes and return volatility (measured by square of daily return). We re-examine his claims by using realized volatility as a more precise estimator of the unobserved volatility, adopting a stationary de-trended trading volume and applying a more recent data sample with robustness tests over time. Our linear Granger causality test shows that there is no causal linear relation running from volume to volatility but there exist an ambiguous causality for the reverse direction. In contrast, we find strong bi-directional nonlinear Granger causality between these two variables. Our results provide strong support for the sequential information theory and offer a promising prospect for developing nonlinear models to predict return volatility using trading volume