基于多变量时间序列的上证市场混沌特征研究

Researches on Chaotic Characteristics of Shanghai Stock Market Based on Multivariable Time Series

以上证A股综合指数日开盘价、最高价及收盘价为研究对象,基于多变量时间序列相空间重构思想,利用平均互信息法、虚假近邻法、G-P算法及小数据量算法等技术给出了上海证券市场的最佳延迟时间、最小嵌入维数、关联维数和最大李雅普诺夫指数等几何不变量,准确地得到了上海证券市场混沌度判定和预测分析的一些重要定量标准,这些定量数据可以为金融理论的研究提供帮助。

This paper took the opening price, the highest price and the closing price of the composite index on the Shanghai A shares as the research objects. Based on the thought of phase - space reconstruction, by the use of the average mutual information method, false neighbor method, G - P algorithm and small - data method, it provided some geometric invariants of the Shanghai stock market, such as the best delay time, minimum embedding dimension, relevance dimension and the largest Lyaptmov exponent etc. ; then accurately obtained some important quantitative criteria for the determination of the degree of market chaos and prediction, which would help the study of financial theory.