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