波兰股票市场波动的非广延统计特征
Nonextensive statistical features of the Polish stock market fluctuations
摘要：
不同时间尺度上收益率分布的统计数据构成了金融动态最具信息性的特征之一。在这里，我们提出了一个系统的研究波兰股票市场指数WIG 20在04.01.1999 - 31.10.2005期间的时间滞后范围从一分钟到一个小时的这些特征。这个市场通常被归类为新兴市场。仍然在最短的时间尺度上研究，我们发现，尾部的收益率分布是一致的逆三次幂律，如以前确定的大多数成熟市场。然而，在研究的时间尺度内，可以追踪到从这一定律向高斯定律的快速而显著的偏离。有趣的是，所观察到的所有形式的分布都可以由单个$q$ -高斯分布组成，它提供了一个令人满意的，同时也是紧凑的表示，表示了收益波动在其变化的所有幅度上的分布。相应的nonextensivity参数$q$被发现系统地减少时，增加的时间尺度。
英文摘要：
The statistics of return distributions on various time scales constitutes one of the most informative characteristics of the financial dynamics. Here we present a systematic study of such characteristics for the Polish stock market index WIG20 over the period 04.01.1999 - 31.10.2005 for the time lags ranging from one minute up to one hour. This market is commonly classified as emerging. Still on the shortest time scales studied we find that the tails of the return distributions are consistent with the inverse cubic power-law, as identified previously for majority of the mature markets. Within the time scales studied a quick and considerable departure from this law towards a Gaussian can however be traced. Interestingly, all the forms of the distributions observed can be comprised by the single $q$-Gaussians which provide a satisfactory and at the same time compact representation of the distribution of return fluctuations over all magnitudes of their variation. The corresponding nonextensivity parameter $q$ is found to systematically decrease when increasing the time scales.
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