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 $\alpha$ or $\beta$, which introduces a bias for small ($\alpha, \beta <0$) or large ($\alpha, \beta >1$) values. Our results show that small values of $v$ are regularly \emph{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.