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 pr
obability 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.
We investigate the statistical properties of the correlation matrix between individual stocks traded in the Korean stock market using the random matrix theory (RMT) and observe how these affect the portfolio weights in the Markowitz portfolio theory.
We find that the distribution of the correlation matrix is positively skewed and changes over time. We find that the eigenvalue distribution of original correlation matrix deviates from the eigenvalues predicted by the RMT, and the largest eigenvalue is 52 times larger than the maximum value among the eigenvalues predicted by the RMT. The $beta_{473}$ coefficient, which reflect the largest eigenvalue property, is 0.8, while one of the eigenvalues in the RMT is approximately zero. Notably, we show that the entropy function $E(sigma)$ with the portfolio risk $sigma$ for the original and filtered correlation matrices are consistent with a power-law function, $E(sigma) sim sigma^{-gamma}$, with the exponent $gamma sim 2.92$ and those for Asian currency crisis decreases significantly.
We study the cascading dynamics immediately before and immediately after 219 market shocks. We define the time of a market shock T_{c} to be the time for which the market volatility V(T_{c}) has a peak that exceeds a predetermined threshold. The casc
ade of high volatility aftershocks triggered by the main shock is quantitatively similar to earthquakes and solar flares, which have been described by three empirical laws --- the Omori law, the productivity law, and the Bath law. We analyze the most traded 531 stocks in U.S. markets during the two-year period 2001-2002 at the 1-minute time resolution. We find quantitative relations between (i) the main shock magnitude M equiv log V(T_{c}) occurring at the time T_{c} of each of the 219 volatility quakes analyzed, and (ii) the parameters quantifying the decay of volatility aftershocks as well as the volatility preshocks. We also find that stocks with larger trading activity react more strongly and more quickly to market shocks than stocks with smaller trading activity. Our findings characterize the typical volatility response conditional on M, both at the market and the individual stock scale. We argue that there is potential utility in these three statistical quantitative relations with applications in option pricing and volatility trading.
Equity activity is an essential topic for financial market studies. To explore its statistical regularities, we comprehensively examine the trading value, a measure of the equity activity, of the 3314 most-traded stocks in the U.S. equity market and
find that (i) the trading values follow a log-normal distribution; (ii) the standard deviation of the growth rate of the trading value obeys a power-law with the initial trading value, and the power-law exponent beta=0.14. Remarkably, both features hold for a wide range of sampling intervals, from 5 minutes to 20 trading days. Further, we show that all the 3314 stocks have long-term correlations, and their Hurst exponents H follow a normal distribution. Furthermore, we find that the Hurst exponent depends on the size of the company. We also show that the relation between the scaling in the growth rate and the long-term correlation is consistent with beta=1-H, similar to that found recently on human interaction activity by Rybski and collaborators.
Publication statistics are ubiquitous in the ratings of scientific achievement, with citation counts and paper tallies factoring into an individuals consideration for postdoctoral positions, junior faculty, tenure, and even visa status for internatio
nal scientists. Citation statistics are designed to quantify individual career achievement, both at the level of a single publication, and over an individuals entire career. While some academic careers are defined by a few significant papers (possibly out of many), other academic careers are defined by the cumulative contribution made by the authors publications to the body of science. Several metrics have been formulated to quantify an individuals publication career, yet none of these metrics account for the dependence of citation counts and journal size on time. In this paper, we normalize publication metrics across both time and discipline in order to achieve a universal framework for analyzing and comparing scientific achievement. We study the publication careers of individual authors over the 50-year period 1958-2008 within six high-impact journals: CELL, the New England Journal of Medicine (NEJM), Nature, the Proceedings of the National Academy of Science (PNAS), Physical Review Letters (PRL), and Science. In comparing the achievement of authors within each journal, we uncover quantifiable statistical regularity in the probability density function (pdf) of scientific achievement across both time and discipline. The universal distribution of career success within these arenas for publication raises the possibility that a fundamental driving force underlying scientific achievement is the competitive nature of scientific advancement.
We investigate the two components of the total daily return (close-to-close), the overnight return (close-to-open) and the daytime return (open-to-close), as well as the corresponding volatilities of the 2215 NYSE stocks from 1988 to 2007. The tail d
istribution of the volatility, the long-term memory in the sequence, and the cross-correlation between different returns are analyzed. Our results suggest that: (i) The two component returns and volatilities have similar features as that of the total return and volatility. The tail distribution follows a power law for all volatilities, and long-term correlations exist in the volatility sequences but not in the return sequences. (ii) The daytime return contributes more to the total return. Both the tail distribution and the long-term memory of the daytime volatility are more similar to that of the total volatility, compared to the overnight records. In addition, the cross-correlation between the daytime return and the total return is also stronger. (iii) The two component returns tend to be anti-correlated. Moreover, we find that the cross-correlations between the three different returns (total, overnight, and daytime) are quite stable over the entire 20-year period.
We study the behavior of U.S. markets both before and after U.S. Federal Open Market Committee (FOMC) meetings, and show that the announcement of a U.S. Federal Reserve rate change causes a financial shock, where the dynamics after the announcement i
s described by an analogue of the Omori earthquake law. We quantify the rate n(t) of aftershocks following an interest rate change at time T, and find power-law decay which scales as n(t-T) (t-T)^-$Omega$, with $Omega$ positive. Surprisingly, we find that the same law describes the rate n(|t-T|) of pre-shocks before the interest rate change at time T. This is the first study to quantitatively relate the size of the market response to the news which caused the shock and to uncover the presence of quantifiable preshocks. We demonstrate that the news associated with interest rate change is responsible for causing both the anticipation before the announcement and the surprise after the announcement. We estimate the magnitude of financial news using the relative difference between the U. S. Treasury Bill and the Federal Funds Effective rate. Our results are consistent with the sign effect, in which bad news has a larger impact than good news. Furthermore, we observe significant volatility aftershocks, confirming a market underreaction that lasts at least 1 trading day.
We study the volatility time series of 1137 most traded stocks in the US stock markets for the two-year period 2001-02 and analyze their return intervals $tau$, which are time intervals between volatilities above a given threshold $q$. We explore the
probability density function of $tau$, $P_q(tau)$, assuming a stretched exponential function, $P_q(tau) sim e^{-tau^gamma}$. We find that the exponent $gamma$ depends on the threshold in the range between $q=1$ and 6 standard deviations of the volatility. This finding supports the multiscaling nature of the return interval distribution. To better understand the multiscaling origin, we study how $gamma$ depends on four essential factors, capitalization, risk, number of trades and return. We show that $gamma$ depends on the capitalization, risk and return but almost does not depend on the number of trades. This suggests that $gamma$ relates to the portfolio selection but not on the market activity. To further characterize the multiscaling of individual stocks, we fit the moments of $tau$, $mu_m equiv <(tau/<tau>)^m>^{1/m}$, in the range of $10 < <tau> le 100$ by a power-law, $mu_m sim <tau>^delta$. The exponent $delta$ is found also to depend on the capitalization, risk and return but not on the number of trades, and its tendency is opposite to that of $gamma$. Moreover, we show that $delta$ decreases with $gamma$ approximately by a linear relation. The return intervals demonstrate the temporal structure of volatilities and our findings suggest that their multiscaling features may be helpful for portfolio optimization.
We investigate the traffic flows of the Korean highway system, which contains both public and private transportation information. We find that the traffic flow T(ij) between city i and j forms a gravity model, the metaphor of physical gravity as desc
ribed in Newtons law of gravity, P(i)P(j)/r(ij)^2, where P(i) represents the population of city i and r(ij) the distance between cities i and j. It is also shown that the highway network has a heavy tail even though the road network is a rather uniform and homogeneous one. Compared to the highway network, air and public ground transportation establish inhomogeneous systems and have power-law behaviors.
We investigate scaling and memory effects in return intervals between price volatilities above a certain threshold $q$ for the Japanese stock market using daily and intraday data sets. We find that the distribution of return intervals can be approxim
ated by a scaling function that depends only on the ratio between the return interval $tau$ and its mean $<tau>$. We also find memory effects such that a large (or small) return interval follows a large (or small) interval by investigating the conditional distribution and mean return interval. The results are similar to previous studies of other markets and indicate that similar statistical features appear in different financial markets. We also compare our results between the period before and after the big crash at the end of 1989. We find that scaling and memory effects of the return intervals show similar features although the statistical properties of the returns are different.
