中国证券市场的非线性多重分形特征研究
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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。
Efficient Market Hypothesis (Efficient Market Hypothesis, EMH) is the bases for modern finance theory, the main idea of EMH is that the market prices reflects all information of market, volatility of market price are independent and unpredictable, the return series obey the random walk Hypothesis, and the distributions of it is normal or logarithm normal distribution. But the abnormal financial vision means that the traditional financial theory exist great limitations, it shows that the capital market is not a linear system, but a nonlinear system. For this we have to understand the basic rules of the capital market with nonlinear fractal theory.
The basic view of nonlinear fractal theory is that the capital markets has fat tail characteristics, market volatility show multiple fractal features. The return series have some persistence and antipersistence character,and different voltility show the character of multifractal character.so the fractal theory can reveal the volatility essence more accurately than that of traditional capital market theory, and reveal basic law in finance market more efficiently also.
With fractal theory and multifractal theory.This paper focuses on the research of Chinese growth enterprize market, the main contends as follows:
(1) Chinese growth ernterprize market (GEM) is analysised with multiple fractal approach, detect the multifractal character in GEM index, GEM industry index and individual listed company in GEM is detected.
(2) Taking the fitting function in multifractal model to deal with China's growth enterprise market, and statistical results are more universality.
(3) The study of multifractal character for return sequence in GEM in china with the moving time window method is given, not only reveal the volatility trend of GEM from macroscopic views, but also from the microscopic views reveal the multifractal characters, and this provide empirical basis for exploring the capital market law
(4) Multifractal feature of Chinese GEM is analysised with random and phase random thoughts,and multifractal reasons are points out.
(5) The corrolation amony Gem index, Gem industry index, and Gem company with multifactal detrended corrolation coupled analysis is revealed.
(6) A new portfolio theory based on multifractal detrended method was put forward, and the empirical adjusted returns got is better than that got with the China securities investment fund portfolio strategy.
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。
Efficient Market Hypothesis (Efficient Market Hypothesis, EMH) is the bases for modern finance theory, the main idea of EMH is that the market prices reflects all information of market, volatility of market price are independent and unpredictable, the return series obey the random walk Hypothesis, and the distributions of it is normal or logarithm normal distribution. But the abnormal financial vision means that the traditional financial theory exist great limitations, it shows that the capital market is not a linear system, but a nonlinear system. For this we have to understand the basic rules of the capital market with nonlinear fractal theory.
The basic view of nonlinear fractal theory is that the capital markets has fat tail characteristics, market volatility show multiple fractal features. The return series have some persistence and antipersistence character,and different voltility show the character of multifractal character.so the fractal theory can reveal the volatility essence more accurately than that of traditional capital market theory, and reveal basic law in finance market more efficiently also.
With fractal theory and multifractal theory.This paper focuses on the research of Chinese growth enterprize market, the main contends as follows:
(1) Chinese growth ernterprize market (GEM) is analysised with multiple fractal approach, detect the multifractal character in GEM index, GEM industry index and individual listed company in GEM is detected.
(2) Taking the fitting function in multifractal model to deal with China's growth enterprise market, and statistical results are more universality.
(3) The study of multifractal character for return sequence in GEM in china with the moving time window method is given, not only reveal the volatility trend of GEM from macroscopic views, but also from the microscopic views reveal the multifractal characters, and this provide empirical basis for exploring the capital market law
(4) Multifractal feature of Chinese GEM is analysised with random and phase random thoughts,and multifractal reasons are points out.
(5) The corrolation amony Gem index, Gem industry index, and Gem company with multifactal detrended corrolation coupled analysis is revealed.
(6) A new portfolio theory based on multifractal detrended method was put forward, and the empirical adjusted returns got is better than that got with the China securities investment fund portfolio strategy.
引文
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