Econophysics and econometrics agree that there is a correlation between volume and volatility in a time series. Using empirical data and their distributions, we further investigate this correlation and discover new ways that volatility and volume interact, particularly when the levels of both...

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...

The distribution of the return intervals $\tau$ between volatilities above a threshold $q$ for financial records has been approximated by a scaling behavior. To explore how accurate is the scaling and therefore understand the underlined non-linear mechanism, we investigate intraday datasets of...

Firms having similar business activities are correlated. We analyze two different cross-correlation matrices C constructed from (i) 30-min price fluctuations of 1000 US stocks for the 2-year period 1994-95 and (ii) 1-day price fluctuations of 422 US stocks for the 35-year period 1962-96. We find...

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 approximated by a scaling function that depends only...

We compare our results on empirical analysis of financial data with simulations of two stochastic models of the dynamics of stock market prices. The two models are (i) the truncated L\'evy flight recently introduced by us and (ii) the ARCH(1) and GARCH(1,1) processes. We find that the TLF well...

We use methods of random matrix theory to analyze the cross-correlation matrix C of price changes of the largest 1000 US stocks for the 2-year period 1994-95. We find that the statistics of most of the eigenvalues in the spectrum of C agree with the predictions of random matrix theory, but there...

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...

Price fluctuations of commodities like cotton and wheat are thought to display probability distributions of returns that follow a L\'evy stable distribution. Recent analysis of stocks and foreign exchange markets show that the probability distributions are not L\'evy stable, a plausible result...

We investigated the network structures of the Japanese stock market through the minimum spanning tree. We defined grouping coefficient to test the validity of conventional grouping by industrial categories, and found a decreasing in trend for the coefficient. This phenomenon supports the...