The dynamics of traded value revisited

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 σ_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 〈 f_i 〉 as H_i = H₀ + γ log 〈 f_i 〉, which is another sign of non-universal behavior. The existence of such liquidity dependent correlations is consistent with the empirical observation that σ_i ∝ 〈 f_i 〉^α, where α is a non-trivial, time scale dependent exponent.