Yet on statistical properties of traded volume: correlation and mutual information at different value magnitudes

In this article we analyse linear correlation and non-linear dependence of traded volume, v, of the 30 constituents of Dow Jones Industrial Average at different value scales. Specifically, we have raised v to some real value α or β, which introduces a bias for small (α,β 1) values. Our results show that small values of v are regularly anti-correlated with values at other scales of traded volume. This is consistent with the high liquidity of the 30 equities analysed and the asymmetric form of the multi-fractal spectrum for traded volume which has supported the dynamical scenario presented by us.