Liu Y, Gopikrishnan P, Cizeau P, Meyer M, Peng C K, Stanley H E
Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Aug;60(2 Pt A):1390-400. doi: 10.1103/physreve.60.1390.
We study the statistical properties of volatility, measured by locally averaging over a time window T, the absolute value of price changes over a short time interval deltat. We analyze the S&P 500 stock index for the 13-year period Jan. 1984 to Dec. 1996. We find that the cumulative distribution of the volatility is consistent with a power-law asymptotic behavior, characterized by an exponent mu approximately 3, similar to what is found for the distribution of price changes. The volatility distribution retains the same functional form for a range of values of T. Further, we study the volatility correlations by using the power spectrum analysis. Both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents. Also, both methods show the presence of a crossover at approximately 1.5 days. In addition, we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 U.S. companies over the two-year period Jan. 1994 to Dec. 1995.
我们研究波动率的统计特性，通过在时间窗口T上进行局部平均来测量，该窗口是在短时间间隔δt内价格变化的绝对值。我们分析了1984年1月至1996年12月这13年期间的标准普尔500股票指数。我们发现波动率的累积分布与幂律渐近行为一致，其特征指数μ约为3，这与价格变化分布的情况类似。对于一系列T值，波动率分布保持相同的函数形式。此外，我们通过使用功率谱分析来研究波动率相关性。两种方法都支持相关函数的幂律衰减，并给出相关标度指数的一致估计。而且，两种方法都表明在大约1.5天处存在交叉。此外，我们通过分析一个包含1994年1月至1995年12月这两年期间美国最大的500家公司所有交易的数据库，将这些结果扩展到了单个公司的波动率。
