  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 $\Delta t$. 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
$N_{\Delta t}$.
