Financial factor influence on scaling and memory of trading volume in stock market (1106.1415v1)

Abstract: We study the daily trading volume volatility of 17,197 stocks in the U.S. 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(\tau) scales with mean interval <\tau> as P_q(\tau)=<\tau>^{-1}f(\tau/<\tau>) and the tails of the scaling function can be well approximated by a power-law f(x)~x^{-\gamma}. We also study the relation between the form of the distribution function P_q(\tau) and several financial factors: stock lifetime, market capitalization, volume, and trading value. We find a systematic tendency of P_q(\tau) associated with these factors, suggesting a multi-scaling feature in the volume return intervals. We analyze the conditional probability P_q(\tau|\tau_0) for $\tau$ following a certain interval \tau_0, and find that P_q(\tau|\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.