中国证券市场的非线性多重分形特征研究

发布时间：2018-04-26 23:42

本文选题：多重分形 + 多重分形去趋势　；参考：《电子科技大学》2012年博士论文

【摘要】：作为现代金融学基础的有效市场假说(Efficient Market Hypothesis,EMH)认为市场价格反映了全部信息,市场价格的波动相互独立且不可预测,收益率服从随机游走假设,收益率分布服从正态或对数正态分布。但是现实中的种种金融异象意味着传统的金融理论存在着很大的局限性,表明现实的资本市场并不如传统理论所描述的那样为一线性系统,而是一非线性系统。为此我们采用非线性分形理论,分析理解资本市场的基本规律。非线性分形理论认为资本市场具有显著的分形结构和尖峰厚尾特征,市场金融序列在一定的标度内具有持续性、反持续性,不同幅度的波动表现出多重分形特征。分形理论比传统资本市场理论能更有效地揭示金融市场的波动本质,能更有效地揭示金融市场的基本规律。本文借鉴分形市场理论和多重分形理论对中国创业板市场进行深度的分析,主要研究内容如下： (1)将多重分形方法引入到中国创业板市场的实证研究中,确认创业板指数、创业板行业和创业板上市公司时间序列的多重标度结构及多重标度特性。 (2)采用多阶函数拟合方法处理中国创业板市场多重分形模型,使研究结果更具普遍性。 (3)利用移动时间窗的方法对中国创业板市场收益序列波动的多重分形特性进行研究,不仅从宏观的角度阐述中国创业板市场收益序列波动的趋势特征,还从微观角度描述了中国创业板市场收益序列多重分形的特性,为探索资本市场规律提供实证依据。 (4)利用随机化及相位随机化思想处理中国创业板市场收益序列的多重分形特性,指出产生多重分形的主要原因。 (5)用多重分形去趋势相关分析法研究创业板行业指数和公司间的相关关系,深度再现不同金融时间序列的相关性特征。 (6)提出并构建基于多重分形去趋势投资组合理论,实证调整收益结果优于中国证券投资基金的组合策略。
[Abstract]:The efficient Market hypothesis (EMH), which is the foundation of modern finance, holds that market price reflects all the information, the fluctuation of market price is independent and unpredictable, and the return rate is assumed to walk from random. Yield distribution from normal or logarithmic normal distribution. However, all kinds of financial anomalies in reality mean that the traditional financial theory has great limitations, which indicates that the real capital market is not a linear system, but a nonlinear system, as described by the traditional theory. Therefore, we use nonlinear fractal theory to analyze and understand the basic laws of capital market. The nonlinear fractal theory holds that the capital market has remarkable fractal structure and peak and thick tail characteristics, and the market financial sequence has the characteristics of persistence, anti-persistence and multi-fractal in certain scale. Fractal theory is more effective than traditional capital market theory in revealing the essence of financial market fluctuation and the basic law of financial market. This paper uses fractal market theory and multifractal theory for reference to analyze the depth of Chinese gem market. The main research contents are as follows: 1) the multifractal method is introduced into the empirical study of the gem market in China. The index of gem, the multi-scale structure and the characteristics of the time series of gem industry and gem listed companies are confirmed. 2) Multi-order function fitting method is used to deal with the multifractal model of Chinese gem market, which makes the research results more universal. 3) using the moving time window method to study the multifractal characteristics of the earnings series fluctuation in China's gem market, not only from the macro point of view, but also to explain the trend characteristics of the volatility of the growth enterprise market income series in China. It also describes the multifractal characteristics of the growth enterprise market income series in China from a micro perspective, which provides an empirical basis for exploring the laws of the capital market. 4) the multifractal characteristics of Chinese gem market income series are dealt with by using the ideas of randomization and phase randomization, and the main causes of multifractal are pointed out. 5) using multifractal detrend correlation analysis method to study the correlation between gem industry index and firms, and to reproduce the correlation characteristics of different financial time series in depth. 6) based on the multifractal detrend portfolio theory, the empirical adjustment result is better than the portfolio strategy of China's securities investment funds.
【学位授予单位】：电子科技大学
【学位级别】：博士
【学位授予年份】：2012
【分类号】：F832.51;F224

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