title: Financial factor influence on scaling and memory of trading volume in stock market.
abstract: 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 τ between volume volatilities above a given threshold q. For different thresholds q, the probability density function P(q)(τ) scales with mean interval 〈τ〉 as P(q)(τ)=〈τ〉(-1)f(τ/〈τ〉), and the tails of the scaling function can be well approximated by a power law f(x)∼x(-γ). We also study the relation between the form of the distribution function P(q)(τ) and several financial factors: stock lifetime, market capitalization, volume, and trading value. We find a systematic tendency of P(q)(τ) associated with these factors, suggesting a multiscaling feature in the volume return intervals. We analyze the conditional probability P(q)(τ|τ(0)) for τ following a certain interval τ(0), and find that P(q)(τ|τ(0)) depends on τ(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.
authors.affiliation: Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: Wei
authors.initials: W
authors.lastname: Li
authors.forename: Fengzhong
authors.initials: F
authors.lastname: Wang
authors.forename: Shlomo
authors.initials: S
authors.lastname: Havlin
authors.forename: H Eugene
authors.initials: HE
authors.lastname: Stanley