1900-2005年道琼斯指数的谱分析及与模型预测周期的比较
Spectral Analysis of Dow Jones Index and Comparison with Model Predicted Cycles During 1900-2005
摘要：
道琼斯指数的日波动表现出分形波动，即在所有时空尺度上都呈现先升后降的锯齿形波动。自相似分形涨落是自然界动力系统的普遍现象，意味着长程时空相关性。动力学系统的明显不可预测的（混沌）波动表现出潜在的秩序与功率谱表现出逆幂律形式，现在被确定为自组织临界性。自组织临界性的物理学尚未确定。作者发展的一般系统理论表明，自相似分形涨落是从量子系统的亚原子动力学到宏观尺度流体流动的所有尺度的动力学系统中的类量子混沌的特征。该模型预测了动力系统分形时空涨落功率谱的统计正态分布的普适逆幂律形式。本文证明了道·琼斯指数100年标准化月间波动的功率谱具有统计正态分布的普适逆幂律形式，与模型预测一致。它表明，预测的最大值和最小值的发生时间在两年之后的数据期间用于研究是可能的使用从历史数据的连续周期谱分析获得的主峰周期性。
英文摘要：
The day-to day fluctuations of Dow Jones Index exhibit fractal fluctuations, namely, a zigzag pattern of successive increases followed by decreases on all space-time scales. Self-similar fractal fluctuations are generic to dynamical systems in nature and imply long-range space-time correlations. The apparently unpredictable (chaotic) fluctuations of dynamical systems exhibit underlying order with the power spectra exhibiting inverse power law form, now identified as self-organized criticality. The physics of self-organized criticality is not yet identified. A general systems theory developed by the author shows that self-similar fractal fluctuations are signatures of quantum-like chaos in dynamical systems of all size scales ranging from the subatomic dynamics of quantum systems to macro-scale fluid flows. The model predicts the universal inverse power-law form of the statistical normal distribution for the power spectra of fractal space-time fluctuations of dynamical systems. In this paper it is shown that the power spectrum of 100 years of normalized month to month fluctuations of Dow Jones index exhibits the universal inverse power law form of the statistical normal distribution consistent with model prediction. It is shown that prediction of times of occurrence of maxima and minima during the two years subsequent to the data period used for the study is possible using the dominant peak periodicities obtained from the continuous periodogram spectral analysis of historic data.
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