SCALING BEHAVIOR IN THE DYNAMICS OF AN ECONOMIC INDEX
SCALING BEHAVIOR IN THE DYNAMICS OF AN ECONOMIC INDEX
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DOI：
10.1038/376046a0
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发表时间：
1995-07-06
期刊：
影响因子：
64.8
通讯作者：
STANLEY, HE
中科院分区：
文献类型：
--
作者：
MANTEGNA, RN;STANLEY, HE
某些物理系统的大尺度动力学性质依赖于大量非线性耦合子系统的动力学演化。例子包括表现出自组织临界性（1）和湍流（2，3）的系统。这样的系统往往表现出空间和时间密封行为幂律行为的一个特定的观察。从地球物理学（4）到生物学（5），在广泛的系统中发现了缩放。在这里，我们探讨了缩放现象发生在经济系统中的可能性，特别是当经济系统受到精确规则的约束时，就像金融市场一样（6-8）。具体来说，我们表明，一个特定的经济指数-标准普尔500指数-的概率分布的标度可以用一个非高斯过程来描述，该过程具有动态，对于分布的中心部分，对应于Levy稳定过程的预测（9-11）。在跨越三个数量级的时间间隔内观察到标度行为，从1,000分钟到1分钟，后者接近于在金融市场中执行交易所需的最小时间。在分布的尾部，下降偏离Levy稳定过程的下降，并且近似为指数，确保（正如人们对价格差异分布所期望的那样）分布的方差是有限的，标度指数在我们的数据的六年期间（1984-89）是非常恒定的，经济指数的这种动态行为应该为开发经济模型提供一个框架。
THE large-scale dynamical properties of some physical systems depend on the dynamical evolution of a large number of nonlinearly coupled subsystems. Examples include systems that exhibit self-organized criticality(1) and turbulence(2,3). Such systems tend to exhibit spatial and temporal sealing behaviour-power-law behaviour of a particular observable. Scaling is found in a wide range of systems, from geophysical(4) to biological(5). Here we explore the possibility that scaling phenomena occur in economic systems-especially especially when the economic system is one subject to precise rules, as is the case in financial market(6-8). Specifically, we show that the scaling of the probability distribution of a particular economic index-the Standard and Poor's 500-can be described by a nongaussian process with dynamics that, for the central part of the distribution, correspond to that predicted for a Levy stable process(9-11). Scaling behaviour is observed for time intervals spanning three orders of magnitude, from 1,000 min to 1 min, the latter being close to the minimum time necessary to perform a trading transaction in a financial market, In the tails of the distribution the fall-off deviates from that for a Levy stable process and is approximately exponential, ensuring that (as one would expect for a price difference distribution) the variance of the distribution is finite, The scaling exponent is remarkably constant over the six-year period (1984-89) of our data, This dynamical behaviour of the economic index should provide a framework within which to develop economic models.