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 $H_i=H_0+γ\log\ev{f_i}$, which is another sign of non-universal behavior. The existence of such liquidity dependent correlations is consistent with the empirical observation that $σ_i\propto\ev{f_i}^α$, where $\alpha$ is a non-trivial, time scale dependent exponent.

5 pages, 4 figures, to appear in Physica A (APFA5 2006), corrected a few errors in references and text

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• Emergence of long memory in stock volatility from a modified Mike-Farmer model
• Complex stock trading network among investors
• Universal price impact functions of individual trades in an order-driven market
• Preferred numbers and the distribution of trade sizes and trading volumes in the Chinese stock market
• Nonuniversal distributions of stock returns in an emerging market
• Endogenous and exogenous dynamics in the fluctuations of capital fluxes: An empirical analysis of the Chinese stock market
• Long-term correlations and multifractal analysis of trading volumes for Chinese stocks
• Scaling and memory in the non-poisson process of limit order cancelation
• Taylor's Law of temporal fluctuation scaling in stock illiquidity