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_Δt for a given stock in a fixed time interval Δt. 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_Δt) displays a power-law decay, and that the time correlations in Q_Δt display long-range persistence. Further, we investigate the relation between Q_Δt and the number of transactions N_Δt in a time interval Δt, and find that the long-range correlations in Q_Δt are largely due to those of N_Δt. Our results are consistent with the interpretation that the large equal-time correlation previously found between Q_Δt and the absolute value of price change |G_Δt| (related to volatility) are largely due to N_Δt.