非线性分析方法在沪市高频时间序列中的应用  

Application nonlinear analysis to high-frequency time series of the Shanghai stock market

作　　者：姜爱萍[1] 黄凤文 

机构地区：[1]同济大学数学系,上海200092 [2]上海城市管理学院,上海200233

出　　处：《成都理工大学学报（自然科学版）》2007年第5期585-588,共4页Journal of Chengdu University of Technology: Science & Technology Edition

摘　　要：为研究高频金融时间序列的可预测性,尝试运用相空间重构和偏差计算分析方法预测t+1时刻股指瞬态变化方向。相空间重构可以保持原高频时间序列的某些信息,这些信息是对系统行为的近似描述。通过这种近似行为的描述,发现当时间t足够大时,即t→∞,系统的特性会被更好地反映出来;运用动态系统偏差来描述系统特性,分析系统的瞬间情况,而这种偏差等价于Jacobian矩阵的迹,它是用来测量无穷小的相空间量V(t)沿着轨迹x(t)的变化率。以沪市综合指数5 min高频数据为实证研究对象,预测t+1时刻股指瞬态变化方向,再和实际股指运动方向做比较,效果比较好。In order to obtain the predictability of high frequency time series, this paper develops state space reconstruction and divergence calculation techniques have been for t＋1 temporal trend of stock index. State space reconstruction techniques preserve certain information on original time series which describes the asymptotic behavior of the system. By describing the asymptotic behavior, the properties of the system will be shown better when time t is large enough, that is,t→∞. Divergence calculation of dynamical system is used to describe the characterisation of system and analyse the temporal trend. The divergence is locally equivalent to the trace of the Jacobian and measures the rate of change of an infinitesimal state space volume V（t） following an orbit x（t）. This paper forecasts the t＋1 temporal trend of the Shanghai stock market composite index based on 5-minute high-frequency time series and gets a satisfied result compared with the actual trend.

关 键 词：非线性分析 相空间重构 偏差计算 无交易成本 预测 

分 类 号：O241.7[理学—计算数学] F830.91[理学—数学]