基于分形与混沌理论的大豆期货市场的特征研究

发布时间：2018-02-28 17:49

本文关键词： 重标极差分析法 Hurst指数分形维相空间重构 Lyapunov指数　出处：《西北农林科技大学》2013年硕士论文　论文类型：学位论文

【摘要】：我国商品期货市场的发展时间较短,只有二十几年,在各方面都处于起步阶段。但即便如此,农产品期货在套期保值和维护市场稳定方面的作用也已经愈发显著。因此,对于金融研究人员来说,如果正确认识农产品期货市场就显得尤为重要。传统上,资本市场的理论基础是有效市场理论(EMT),它的假设基础为线性基础,认为资本市场的收益率是服从正态分布的。然而,频繁发生的金融危机让学者们对资本市场背后的假设提出了种种质疑。而非线性科学的快速发展则为学者们研究金融市场提供了一个更加有效的工具,使人们不再拘泥于线性理论和有效市场的束缚。本文以近些年的研究为基础,以两种比较流行的非线性分析方法——分形理论与混沌理论为基础,对我国大豆期货市场的价格和成交量波动进行考察和分析,并首次对大豆期货的成交量进行了研究。首先,运用重标极差分析法(Rescaled Range Analysis, R/S)对我国大豆期货市场整体和单个大豆期货的收益率及成交量进行了实证分析,结果表明：大豆期货整体收益率序列和成交量序列的Hurst指数明显大于0.5,即表现出分形特征。对单个大豆期货合约的研究表明,尽管并非每个品种都表现出明显的分形特征,但大多数的期货品种的分形特征较为明显。随后,采用打乱数据的方法对分形结果进行了检验,打乱后数据的Hurst指数小于打乱前的Hurst指数,表明原始序列存在短期记忆性,证明了非周期循环的存在。第二,采用相空间投影的方法对大豆期货的价格序列和成交量序列进行了研究。首先采用自相关函数法分别计算了价格序列和成交量序列的延滞时间T和嵌入维m,随后采用小数据量算法计算了大豆期货价格波动和成交量波动的混沌特征参数。结果表明：我国大豆期货市场的价格序列的最大Lyapunov指数为正数,同时,其关联维数为非整数,这表明,我国大豆期货市场存在典型的混沌特征；而成交量波动虽然具有正的最大Lyapunov指数,但其关联维数较小,说明其具有弱混沌特征。作为对比,本文第四部分计算了对数收益率序列的混沌特征,其相空间投影表现出一定的随机性,表明收益率序列的混沌特征并不明显。因此,将收盘价作为研究价格序列的参数较为合适。综上,我国大豆期货市场的价格序列具有明显的分形特征和混沌特征；成交量序列呈现出明显的分形特征和弱的混沌特征。这表明,采用传统的以线性模型为基础的有效市场理论无法解释我国大豆期货市场的价格及成交量的变化。
[Abstract]:The development of commodity futures market in China is relatively short, only more than 20 years, and it is at the initial stage in every aspect. But even so, the role of agricultural product futures in hedging and maintaining market stability has become more and more significant. For financial researchers, if the correct understanding of the agricultural futures market is particularly important. Traditionally, the theoretical basis of the capital market is the efficient market theory (EMTT), which assumes that the return rate of the capital market is normally distributed. Frequent financial crises have made scholars question the assumptions behind capital markets. The rapid development of nonlinear science has provided a more effective tool for scholars to study financial markets. So that people are no longer bound to linear theory and efficient market constraints. Based on the research in recent years, based on two popular nonlinear analysis methods-fractal theory and chaos theory, this paper investigates and analyzes the fluctuation of price and turnover of soybean futures market in China. The trading volume of soybean futures was studied for the first time. First of all, we use rescaled Range analysis (R / S) to analyze the yield and turnover of soybean futures in China. The results show that the Hurst index of the whole yield series and volume series of soybean futures is more than 0.5, that is to say, it shows fractal characteristics. The study of single soybean futures contract shows that, although not every variety shows obvious fractal characteristics, However, the fractal characteristics of most futures varieties are obvious. Then, the fractal results are tested by the method of scrambling data. The Hurst index of the disturbed data is smaller than that of the Hurst index before scrambling, which indicates that the original sequence has short-term memory. The existence of aperiodic cycles is proved. Second, The price sequence and volume sequence of soybean futures were studied by the method of phase space projection. Firstly, the delay time T and embedded dimension of price sequence and volume sequence were calculated by autocorrelation function method. The chaotic characteristic parameters of price fluctuation and trading volume fluctuation of soybean futures are calculated by using the algorithm of small amount of data. The results show that the maximum Lyapunov index of the price series of soybean futures market in China is a positive number. At the same time, the correlation dimension is non-integer, which indicates that there are typical chaotic characteristics in the soybean futures market in China, while the volatility of trading volume has a positive maximum Lyapunov index, but its correlation dimension is small, which indicates that it has weak chaotic characteristics. By contrast, the chaotic characteristics of logarithmic rate of return series are calculated in the 4th part of this paper. The phase space projection shows a certain randomness, which indicates that the chaotic characteristics of the return sequence are not obvious. It is more appropriate to take the closing price as the parameter of the study price sequence. In summary, the price sequence of soybean futures market in China has obvious fractal and chaotic characteristics, while the trading volume series has obvious fractal characteristics and weak chaotic characteristics. The traditional efficient market theory based on linear model can not explain the change of price and turnover of soybean futures market in China.
【学位授予单位】：西北农林科技大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F724.5

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