Scaling of the distribution of fluctuations of financial market indices
Scaling of the distribution of fluctuations of financial market indices
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DOI：
10.1103/physreve.60.5305
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发表时间：
1999-11-01
影响因子：
2.4
通讯作者：
Stanley, HE
中科院分区：
文献类型：
--
作者：
Gopikrishnan, P;Plerou, V;Stanley, HE
我们通过分析三个不同的数据库，研究了S&P 500指数在时间尺度Δ t上的波动分布。数据库（一）包含约1200000条记录，采样时间间隔为1分钟，为1984-1996年的IS年期间，数据库（二）包含8686日记录的35年期间1962-1996年，数据库（三）包含852个月的71年期间1926-1996年的记录。我们计算收益率在时间尺度Delta t上的概率分布，其中Delta t的变化近似为10（4）倍-从1分钟到超过一个月。我们发现，小于或等于4 d（1560 min）的Delta t分布符合幂律渐近行为，其特征在于指数α近似为3，远远超出稳定的Levy区域0 < alpha < 2。为了检验标准普尔结果的稳健性，我们对其他两个金融市场指数进行了平行分析。数据库（iv）包含1984-1997年18年期间的NIKKEI指数的3560个每日记录，数据库（v）包含1980-1997年18年期间的恒生指数的4649个每日记录。我们发现alpha的估计值与描述标准普尔500指数日收益率分布的估计值一致。这些分布的缩放的一个可能的原因是波动率的自相关函数的长期持续性。对于时间尺度长于（Δ t）（x）近似4 d，我们的结果是一致的高斯行为的缓慢收敛。[S1063-651X（99）11211-X]。
We study the distribution of fluctuations of the S&P 500 index over a time scale Delta t by analyzing three distinct databases. Database (i) contains approximately 1200000 records, sampled at 1-min intervals, for the IS-year period 1984-1996, database (ii) contains 8686 daily records for the 35-year period 1962-1996, and database (iii) contains 852 monthly records for the 71-year period 1926-1996. We compute the probability distributions of returns over a time scale Delta t, where Delta t varies approximately over a factor of 10(4)-from 1 min up to more than one month. We find that the distributions for Delta t less than or equal to 4 d (1560 min) are consistent with a power-law asymptotic behavior, characterized by an exponent alpha approximate to 3, well outside the stable Levy regime 0 < alpha < 2. To test the robustness of the S&P result, we perform a parallel analysis on two other financial market indices. Database (iv) contains 3560 daily records of the NIKKEI index for the 18-year period 1984-1997, and database (v) contains 4649 daily records of the Hang-Seng index for the Is-year period 1980-1997. We find estimates of alpha consistent with those describing the distribution of S&P 500 daily returns. One possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility. For time scales longer than (Delta t)(x) approximate to 4 d, our results are consistent with a slow convergence to Gaussian behavior. [S1063-651X(99)11211-X].