Statistical properties of the volatility of price fluctuations.

摘要: We study the statistical properties of volatility, measured by locally averaging over a time window T, absolute value price changes short interval $\ensuremath{\Delta}t.$ analyze S 500 stock index for 13-year period Jan. 1984 to Dec. 1996. find that cumulative distribution volatility is consistent with power-law asymptotic behavior, characterized an exponent $\ensuremath{\mu}\ensuremath{\approx}3,$ similar what found changes. The retains same functional form range values T. Further, we correlations using power spectrum analysis. Both methods support law decay correlation function and give estimates relevant scaling exponents. Also, both show presence crossover at approximately $1.5$ days. In addition, extend these results individual companies analyzing data base comprising all trades largest U.S. two-year 1994 1995.