中国股市主板、中小板及创业板的分形分析

发布时间：2018-02-26 14:41

本文关键词： 股票指数 MF-DFA 单分形多重分形市场波动性　出处：《兰州大学》2017年硕士论文　论文类型：学位论文

【摘要】：由于中国股市存在着大量非理性的交易者以及不完备的政策体系等因素,导致中国股市频频出现异常波动。近年来,经过国内外相关专家学者不断深入的探索,认为分形理论比有效市场理论更能细致刻画出资本市场的波动本质,同时也能更加深层次地剖析资本市场的内在规律。因此本文运用分形理论来研究中国股市主板、中小板及创业板三大板块的波动特征。本文的研究思路如下:首先对三大板块股指收益率及成交量进行了正态性检验,其次,依据各板块股指收益率和成交量这两个指标,就各板块股票指数依次展开了单分形和多重分形的分析,最后从横向和纵向两个维度,全面分析了各板块分形特征之间的差异。本次研究的主要结论为:(1)三大板块的日收益率时间序列均表现出不同程度的尖峰厚尾特性,相比于中小板及创业板,主板信息分布更集中,表明其易变性和波动性更为显著,而中小板及创业板的信息分布相对更为均匀。(2)主板指数、中小板指数及创业板指数日收益率均存在显著的长期记忆性。创业板的Hurst指数最低,所以创业板中掺杂的噪声相对是比较少的,也即股指有更强的持续涨跌的趋势。主板与创业板的Hurst指数相近,中小板的Hurst指数最高,说明中小板价格连续涨跌的趋势不够明显。(3)中国股市对初始价格保持敏感且具有依赖性,遵循一个有偏的随机过程,不服从随机游走模型,还没有到达弱式有效状态,是一个分形市场。(4)中国股市三大板块收益率及成交量指标的多重分形谱均呈向右的钩状,说明股指收益率及成交量都呈现出多重分形特性,分形方法能更好地揭示中国股票市场三大板块的波动性现象。
[Abstract]:Due to the existence of a large number of irrational traders and incomplete policy systems in the Chinese stock market, the Chinese stock market frequently fluctuates. In recent years, the relevant experts and scholars at home and abroad have continued to explore deeply. It is believed that fractal theory can describe the essence of capital market fluctuation more carefully than efficient market theory, and at the same time, it can analyze the inherent law of capital market more deeply. Therefore, this paper uses fractal theory to study the main board of Chinese stock market. The research ideas of this paper are as follows: firstly, the return rate and turnover of the three major stock indexes are tested normality, and secondly, according to the two indexes of stock index yield and turnover of each plate, The single-fractal and multifractal analysis of the stock index of each plate is carried out in turn, and finally, from the horizontal and vertical dimensions, The main conclusion of this study is that the time series of daily yield of the three major plates show different degree of peak and thick tail characteristics, compared with the small and medium-sized boards and the growth Enterprise Board, the main conclusion of this study is that the time series of daily yield of the three major plates show different degrees of peak and thick tail characteristics, compared with the small and medium-sized boards and the growth Enterprise Board. The information distribution of the main board is more concentrated, which indicates that the variability and volatility of the main board are more significant, while the information distribution of the small and medium-sized board and the growth enterprise board is relatively more uniform. Both the small and medium board index and the growth enterprise board index have significant long-term memory. The Hurst index of the growth enterprise board is the lowest, so the noise in the growth enterprise board is relatively less. That is, the stock index has a stronger trend of continuous rise and fall. The Hurst index of the main board is similar to that of the growth enterprise board, and the Hurst index of the small and medium-sized board is the highest. It shows that the trend of continuous rise and fall of small and medium board prices is not obvious enough) the Chinese stock market is sensitive to and dependent on the initial price, follows a biased stochastic process, does not accept the random walk model, and has not yet reached a weak effective state. It is a fractal market. (4) the multifractal spectrum of the return rate and the turnover index of the three major plates of the Chinese stock market are all hooks to the right, indicating that both the return rate of the stock index and the trading volume are multifractal. Fractal method can better reveal the volatility of the three major sectors in China's stock market.
【学位授予单位】：兰州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F832.51

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