The dynamics of traded value revisited

Abstract

We conclude from an analysis of high resolution NYSE data that the distribution of the traded value $f_i$ (or volume) has a finite variance $\sigma_i$ for the very large majority of stocks $i$, and the distribution itself is non-universal across stocks. The Hurst exponent of the same time series displays a crossover from weakly to strongly correlated behavior around the time scale of 1 day. The persistence in the strongly correlated regime increases with the average trading activity $\ev{f_i}$ as $H_i=H_0+\gamma\log\ev{f_i}$, which is another sign of non-universal behavior. The existence of such liquidity dependent correlations is consistent with the empirical observation that $\sigma_i\propto\ev{f_i}^\alpha$, where $\alpha$ is a non-trivial, time scale dependent exponent.