基于混沌理论的中国金融市场投资决策研究

发布时间：2018-07-31 15:48

【摘要】：近年来，作为市场经济体系的有机构成部分，全球金融市场的规模急剧扩大，重要性日益凸显。作为一个新兴的市场，中国金融市场的发展更是举世瞩目。中国A股市场市值已跃居全球第二；而中国的期货市场经过最近十多年的蓬勃发展，已成为全球第一大商品期货市场，国内首个金融期货品种——沪深300指数期货也在2010年上市。中国的黄金市场虽然起步较晚，但随着国内投资者避险意识的觉醒，现在无论是交易量还是市场影响力都有了长足的进步。如今在中国，金融投资已逐步成为个人、企业乃至政府的重要理财工具。在金融分析和投资决策领域，长期以来一直以有效市场假说和建立在其基础之上的资本资产定价模型为理论基石。然而随着时代的发展，金融市场的分形、混沌等复杂特性逐渐为人所知。本文即以混沌理论为基础，对中国的股票、期货、黄金等金融市场进行系统的研究，以期揭示这个新兴市场的内在规律，探讨有效的投资决策方法。本文研究的主要内容包括以下几个方面： 1）中国金融市场的混沌性检验。在数据预处理上，采用对数线性去趋势和收益率两种方法对数据进行了平稳化处理。对于时间上不连续的期货市场品种，新设计了最大交易量复权法，，保证价格的连续性和代表性。然后对平稳化后的序列以R/S分析和BDS检验以及递归图方法进行非线性和确定性检验。之后再进行相空间重构，考察其混沌不变量。通过这些分析，弥补了以前国内期货市场大部分品种和黄金市场都未进行混沌识别的不足，得出中国金融市场中普遍存在混沌的结论。 2）中国金融市场的噪声处理研究。主要从两个方面研究了中国金融市场市场的噪声处理。一是噪声估计，以常用的关联积分法、粗糙纹理熵方法、小波法等估计了我国金融市场的噪声水平。并利用小波变换的方差分解功能对白噪声的小波系数方差进行分析，提出一种新的噪声估计方法。二是噪声平滑方面，分析了非线性局部平均法和局部投影法，重点研究了小波软阈值去噪方法，提出基于小波方差分解的新阈值去噪方法，并用Lorenz、Chen等混沌系统数据进行检验。其后运用该方法对国内金融市场中有代表性的几个品种的价格序列进行噪声平滑处理，验证了有效性。最后，以上证指数日收盘价格序列作为样本，通过一天预测再反平稳化以比较均方根误差的方法，比较了各种噪声平滑方法在金融市场的实际去噪效果。 3）中国金融市场的混沌预测研究。噪声估计和平滑处理的基础上，首先用Lyapunov指数法对我国金融市场的几个代表性品种进行预测实证。然后研究了Valterra级数自适应预测模型在中国金融市场的应用，并使用递推最小二乘算法（RLS）来提高Volterra预测模型的预测精度。在对国内几个金融市场的实际预测表明，基于Valterra级数的自适应预测模型效果明显优于Lyapunov指数预测法，但是该方法存在稳定性差的问题。一般常用的神经网络模型多属于静态前馈的处理模式，本文将递归预测器神经网络应用到对金融市场的预测中。在网络训练上，提出用遗传算法优化网络的阈值、权值以及激发函数的幅值和斜率。和其他典型的神经网络预测方法——BP神经网络、径向基函数神经网络等的比较结果表明，该方法有较好的预测效果，而且稳定性强，是适合中国金融市场决策分析的有效预测方法。 4）中国金融市场的混沌交易模型和投资组合模型研究。技术分析是当今最为广泛使用的金融投资分析工具。文章首先在混沌与分形的视角下，重新阐释了技术分析的三大假设，提出混沌分形理论的发展夯实了技术分析的理论基础。其后把混沌预测与技术分析模型结合起来，产生了一些混沌交易模型，包括移动平均交易规则、滤子法则等，并进行了实证分析。混合交易模型是基于遗传规划，结合混沌预测而构建的。对金融市场的实证检验的结果表明，该模型无论在超额收益率还是稳定性上都要优于传统的交易规则模型。最后，文章基于非线性和行为金融理论，提出了基于损失规避的效用函数-偏度投资组合模型，发现该模型的表现要优于其他传统的投资组合模型。
[Abstract]:In recent years, as an organic part of the market economy, the scale of the global financial market has expanded rapidly and its importance has become increasingly prominent. As a new market, the development of China's financial market has attracted worldwide attention. The market value of China's A share market has leaped into second of the world, and China's futures market has developed vigorously after the last more than 10 years, It has become the world's largest commodity futures market, the first domestic financial futures variety - Shanghai and Shenzhen 300 index futures also listed in 2010. Although China's gold market started late, but with the awakening of domestic investors' awareness of risk avoidance, both the trading volume and market impact have made considerable progress. Now, in China, finance Investment has gradually become an important financial tool for individuals, enterprises and even the government.
In the field of financial analysis and investment decision, the capital asset pricing model based on the effective market hypothesis has long been the cornerstone of the theory. However, with the development of the times, the fractal and chaos of the financial market are gradually known. This paper is based on the chaos theory, the stock, futures, yellow of China. The financial markets such as gold are systematically studied in order to reveal the inherent law of this emerging market and explore effective investment decision-making methods.
The main contents of this paper include the following aspects:
1) chaos test in China's financial market. In data preprocessing, the data is stabilized with two methods of logarithmic linear trend and rate of return. R/S analysis, BDS test and recursive graph method are used for nonlinear and deterministic test. Then phase space reconstruction is carried out to investigate its chaotic invariants. Through these analyses, the shortcomings of the previous domestic futures market and the gold market have not been identified, and the general chaos in China's financial market is concluded. Theory.
2) noise treatment in China's financial market. The noise treatment of China's financial market is studied from two aspects. One is noise estimation. The noise level of China's financial market is estimated by using the commonly used correlation integral method, rough texture entropy method, wavelet method and so on. And the wavelet transform is used to analyze the white noise in the wavelet transform. The coefficient variance is analyzed and a new noise estimation method is proposed. Two is the noise smoothing, the nonlinear local mean method and the local projection method are analyzed. The wavelet soft threshold denoising method is studied, and the new threshold de-noising method based on the wavelet variance decomposition is proposed, and the data of the chaotic system such as Lorenz and Chen are tested. Using this method, the price sequence of several representative varieties in domestic financial market is smoothed and smoothed, and the validity is verified. Finally, taking the daily closing price sequence of Shanghai stock index as a sample, the method of comparing the square root error with a day prediction is predicted and compared with the actual method of noise smoothing in the financial market. De-noising effect.
3) chaos prediction in China's financial market. On the basis of noise estimation and smoothing, the Lyapunov index method is used to predict several representative varieties of the financial market in China. Then the application of Valterra series adaptive prediction model in China's financial market is studied, and the recursive least square algorithm (RLS) is used to improve the financial market. The prediction accuracy of the high Volterra prediction model. The actual prediction of several domestic financial markets shows that the effect of the adaptive prediction model based on Valterra series is obviously superior to the Lyapunov index prediction method, but the method has the problem of poor stability. The recursive predictor neural network is applied to the prediction of the financial market. In the network training, the genetic algorithm is proposed to optimize the threshold of the network, the weight and the amplitude and slope of the excitation function, and other typical neural network prediction methods, such as the BP neural network, the radial basis function neural network, and so on. Good prediction effect and strong stability is an effective forecasting method suitable for China's financial market decision analysis.
4) the chaotic trading model and portfolio model in China's financial market. Technical analysis is the most widely used financial investment analysis tool. The article first reinterprets the three hypotheses of technical analysis in the perspective of chaos and fractal, and puts forward that the development of chaotic fractal theory consolidating the theoretical basis of technical analysis. Chaos prediction and technical analysis model are combined to produce some chaotic trading models, including the moving average trading rules, filter rules and so on. The mixed transaction model is based on genetic programming and combined with chaotic prediction. The results of the empirical test on financial markets show that the model is overcharged. The benefit rate or stability is better than the traditional trading rule model. Finally, based on the nonlinear and behavioral finance theory, the utility function bias portfolio model based on loss avoidance is proposed, and it is found that the model is better than the other traditional portfolio model.
【学位授予单位】：南京航空航天大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：F832.51

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