Jones industrial average index (DJIA) for different periods of their historical daily data. We have analyzed the returns … autocorrelation function (ACF) and used detrended fluctuation analysis (DFA) to study returns variations. We also analyze the … volatility, mean value and standard deviation of both markets and compare their evolution. We conclude from the overall result of …

In this study, we investigate the statistical properties of the stock return volatility, defined as the absolute value … of the logarithmic relative price changes. We show examples of power-law and of exponential-law for the volatility …

. We apply these statistics to the distribution of returns of one century of daily data for the Dow Jones Industrial … suggest that the structure of the tails of the distributions of returns is more complex than usually assumed; it is clearly …

We study the probability distribution of stock returns at mesoscopic time lags (return horizons) ranging from about an … function is determined by the variance of returns, which increases proportionally to the time lag. At longer times, the … analytical solution of the Heston model with stochastic volatility. …

In high frequency financial data not only returns but also waiting times between trades are random variables. In this …