Financial factor influence on scaling and memory of trading volume in stock market

We study the daily trading volume volatility of 17 197 stocks in the US stock markets during the period 1989–2008 and analyze the time return intervals $\tau$ between volume volatilities above a given threshold $q$. For different thresholds $q$, the probability density function $P_q\left(\tau \right)$ scales with mean interval $\langle \tau \rangle$ as $P_q\left(\tau \right)={\langle \tau \rangle }^{-1}f(\tau /\langle \tau \rangle )$, and the tails of the scaling function can be well approximated by a power law $f\left(x\right)\sim x^{-\gamma }$. We also study the relation between the form of the distribution function $P_q\left(\tau \right)$ and several financial factors: stock lifetime, market capitalization, volume, and trading value. We find a systematic tendency of $P_q\left(\tau \right)$ associated with these factors, suggesting a multiscaling feature in the volume return intervals. We analyze the conditional probability $P_q\left(\tau \right|{\tau }_0)$ for $\tau$ following a certain interval ${\tau }_0$, and find that $P_q\left(\tau \right|{\tau }_0)$ depends on ${\tau }_0$ such that immediately following a short (long) return interval a second short (long) return interval tends to occur. We also find indications that there is a long-term correlation in the daily volume volatility. We compare our results to those found earlier for price volatility. DOI: http://dx.doi.org/10.1103/PhysRevE.84.046112 ©2011 American Physical Society