我国股票指数的混沌时间序列分析

发布时间：2018-01-04 11:32

本文关键词：我国股票指数的混沌时间序列分析　出处：《中南大学》2013年硕士论文　论文类型：学位论文

【摘要】：本文以我国股票市场的两种股票指数数据作为研究对象,首先对这两种时间序列进行混沌性质的判定,得出均为混沌时间序列,再用混沌预测法对其进行预测。本文的主要工作安排如下：第一部分介绍本文用到的基础知识与方法。第二部分对两种指数时间序列进行检验。首先应用功率谱法发现数据结构为非周期运动,频数直方图分析这两组数据与正态分布之间存在差异,PCA分析法则表明数据为非噪声序列且具有混动性质。这三种定性分析法判定这两组时间序列都有混沌性质。在定性分析的基础上,再用统计特征量如Lyapunov指数、关联维数与Kolmogorov熵等定量分析判定这两种指数的混沌性质。本文采用C-C法进行相空间重构；G-P算法计算关联维数和Kolmogorov熵发现这两种序列的关联维具有收敛性,Kolmogorov熵为正数；采用Wolf法和小数据量法计算最大Lyapunov指数,这两种方法计算的最大Lyapunov指数均为正数；这样,进一步说明这两种指数序列处于混沌状态。第三部分是在第二部分得出两种股票指数数据具有混沌性质后,采用局域预测法和基于最大Lyapunov指数预测对两种序列分别进行100步和20步的预测,并将预测值与真实值进行比较,得出方差。结果表明局域法比之最大Lyapunov指数法预测步数短,在第一步预测和20步预测中效果要好于最大Lyapunov指数法,而后者在100步预测中效果好,且其误差波动平缓。
[Abstract]:In this paper, two kinds of stock index data in China's stock market are taken as the research object. Firstly, the chaotic properties of the two time series are determined, and the chaotic time series are obtained. The main work of this paper is as follows: The first part introduces the basic knowledge and methods used in this paper. In the second part, two kinds of exponential time series are tested. Firstly, the power spectrum method is used to find that the data structure is aperiodic, and the frequency histogram is used to analyze the difference between the two groups of data and normal distribution. The PCA analysis rule shows that the data is a non-noise sequence and has the property of mixing. These three qualitative analysis methods determine that the two groups of time series have chaotic properties. On the basis of qualitative analysis. The chaotic properties of the two indices are determined by quantitative analysis such as Lyapunov exponent, correlation dimension and Kolmogorov entropy. In this paper, the phase space reconstruction is carried out by C-C method. When G-P algorithm calculates correlation dimension and Kolmogorov entropy, it is found that the correlation dimension of these two sequences is convergent and Kolmogorov entropy is positive. The maximum Lyapunov exponent is calculated by the Wolf method and the small data method. The maximum Lyapunov exponent calculated by these two methods is both positive. This further shows that the two exponential sequences are in a chaotic state. The third part is in the second part of the two stock index data with chaotic properties. The local prediction method and the prediction based on the maximum Lyapunov exponent were used to predict the two kinds of sequences, and the predicted values were compared with the real values. The results show that the local method has shorter prediction steps than the maximum Lyapunov exponent method and is better than the maximum Lyapunov exponent method in the first step prediction and 20 step prediction. The latter has good effect in 100 step prediction, and its error fluctuation is gentle.
【学位授予单位】：中南大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F832.51;F224

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