Statistical properties of share volume traded in financial markets

We quantitatively investigate the ideas behind the often-expressed adage “it takes volume to move stock prices,” and study the statistical properties of the number of shares traded $Q_{\Delta t}$ for a given stock in a fixed time interval $\Delta t.\mathrm{}$ We analyze transaction data for the largest 1000 stocks for the two-year period 1994–95, using a database that records every transaction for all securities in three major US stock markets. We find that the distribution ${P(Q}_{\Delta t})$ displays a power-law decay, and that the time correlations in $Q_{\Delta t}$ display long-range persistence. Further, we investigate the relation between $Q_{\Delta t}$ and the number of transactions $N_{\Delta t}$ in a time interval $\Delta t,$ and find that the long-range correlations in $Q_{\Delta t}$ are largely due to those of $N_{\Delta t}.$ Our results are consistent with the interpretation that the large equal-time correlation previously found between $Q_{\Delta t}$ and the absolute value of price change $|G_{\Delta t}|$ (related to volatility) are largely due to $N_{\Delta t}.$