沪深300股指内在复杂性分析及预测研究
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摘要
金融系统是开放的复杂系统,其内部的各个经济变量之间存在错综复杂的关系。在金融系统中,既存在线性关系,也存在非线性关系。线性框架下的研究理论体系推动了金融市场的发展,然而随着实证研究和金融学理论的发展,越来越多的证据表明仅仅用线性方法己经不能很好的解释金融市场的波动。20世纪80年代以后,许多学者开始探寻应用非线性方法解释复杂的金融现象并对其演化过程进行预测,由于使用的研究方法和工具不同,研究结论的差别也很大。本文应用混沌理论和神经网络预测技术对沪深300股指序列进行了非线性检验和预测。研究内容大致包括下面几部分:
1.综述了近年来比较有代表性的金融时间序列混沌特征的检验方法,利用功率谱、递归图、Cao方法、替代数据等方法计算了沪深300部分股指时间序列的有关数据,并根据结果对其混沌特性进行了判定。
2.研究了不同特性时序数据的复原图和相干复原图的特性,并在此基础上研究了沪深300股票指数的复杂度及状态分类;应用Wolf算法对沪深300股指序列中某些特殊股指数据的最大Lyapunov指数进行了计算,并给出了计算结果所代表的含义。
3.利用非线性自相关模型对上海证券市场510050号股票数据的不同价格数据进行建模、对模型中参数辨识等工作并基于RBF神经网络的局域预测法对沪深300中的万科A股股指数据的各种价格进行了预测。
4.介绍了艾略特波浪理论并根据该理论分析了市场情绪与市场行为的反应;在此基础上给出了市场位置相对浪级特征的判断方法,并以此为依据对股票市场后市宏观走势进行了预测。
本文针对金融系统的非线性特点,将混沌理论、神经网络预测技术以及波浪理论应用到沪深300股指序列预测的研究中,结果表明这些理论能够有效地对金融市场波动进行非线性分析和预测,为金融时间序列的非线性建模和预测提供了重要的理论和实证依据。
In an open complex system, there are intricate relationships among the economic variables in the financial system, and both linear and nonlinear relationships exist in it. The financial theory system within the linear framework propels the financial market forward, however, more and more evidence demonstrates that the fluctuation of financial market cannot be explained clearly only by linear method. Since the 1980’s, many scholars have been exploring and looking for some nonlinear methods to explain financial phenomenon and forecast the price evolvement in financial market. Yet the conclusions are different due to the different methods and utilities. In this paper, time series of HS300 stock index is analyzed and forecasting based on the theory of chaos and neural network. The paper mainly includes the following integrations:
1. The representative methods of detecting chaos in financial time series and are introduced and the relevant data about HS300 stock index are calculated via the methods of power spectrum, RPS, Cao, surrogate-data and so on. The obtained results are used to detect chaos in the time series.
2. The characters of RP and CRP of various time series are studied, and on that basis, the complexity and the state classification are analyzed. The maximal Lyapunov index of the data of some HS300 stock index are calculated via the method of Wolf and the meaning of the results are also presented.
3. The nonlinear autocorrelated model for the stock data of No. 510050 of SSE is established and the parameters are identified. Various prices of Vanke A of SH300 are forecasted via the local prediction method based on RBF neural network.
4. Elliott wave theory is introduced and used to analyze the response of market sentiment and behavior. Also, the method of identifying the market position according to characters of the wave level is provided and is used to forecasting the macro trend of the stock market.
Considering the nonlinear characteristics of financial market, the theories of chaos, forecasting method based on neural network and Elliott wave theory are applied to analyze HS300 stock index time series. The results show these theories and methods can explain and forecast the fluctuation of financial market and provide important theoretical and empirical basis for nonlinear modeling and forecasting of financial time series.
1.综述了近年来比较有代表性的金融时间序列混沌特征的检验方法,利用功率谱、递归图、Cao方法、替代数据等方法计算了沪深300部分股指时间序列的有关数据,并根据结果对其混沌特性进行了判定。
2.研究了不同特性时序数据的复原图和相干复原图的特性,并在此基础上研究了沪深300股票指数的复杂度及状态分类;应用Wolf算法对沪深300股指序列中某些特殊股指数据的最大Lyapunov指数进行了计算,并给出了计算结果所代表的含义。
3.利用非线性自相关模型对上海证券市场510050号股票数据的不同价格数据进行建模、对模型中参数辨识等工作并基于RBF神经网络的局域预测法对沪深300中的万科A股股指数据的各种价格进行了预测。
4.介绍了艾略特波浪理论并根据该理论分析了市场情绪与市场行为的反应;在此基础上给出了市场位置相对浪级特征的判断方法,并以此为依据对股票市场后市宏观走势进行了预测。
本文针对金融系统的非线性特点,将混沌理论、神经网络预测技术以及波浪理论应用到沪深300股指序列预测的研究中,结果表明这些理论能够有效地对金融市场波动进行非线性分析和预测,为金融时间序列的非线性建模和预测提供了重要的理论和实证依据。
In an open complex system, there are intricate relationships among the economic variables in the financial system, and both linear and nonlinear relationships exist in it. The financial theory system within the linear framework propels the financial market forward, however, more and more evidence demonstrates that the fluctuation of financial market cannot be explained clearly only by linear method. Since the 1980’s, many scholars have been exploring and looking for some nonlinear methods to explain financial phenomenon and forecast the price evolvement in financial market. Yet the conclusions are different due to the different methods and utilities. In this paper, time series of HS300 stock index is analyzed and forecasting based on the theory of chaos and neural network. The paper mainly includes the following integrations:
1. The representative methods of detecting chaos in financial time series and are introduced and the relevant data about HS300 stock index are calculated via the methods of power spectrum, RPS, Cao, surrogate-data and so on. The obtained results are used to detect chaos in the time series.
2. The characters of RP and CRP of various time series are studied, and on that basis, the complexity and the state classification are analyzed. The maximal Lyapunov index of the data of some HS300 stock index are calculated via the method of Wolf and the meaning of the results are also presented.
3. The nonlinear autocorrelated model for the stock data of No. 510050 of SSE is established and the parameters are identified. Various prices of Vanke A of SH300 are forecasted via the local prediction method based on RBF neural network.
4. Elliott wave theory is introduced and used to analyze the response of market sentiment and behavior. Also, the method of identifying the market position according to characters of the wave level is provided and is used to forecasting the macro trend of the stock market.
Considering the nonlinear characteristics of financial market, the theories of chaos, forecasting method based on neural network and Elliott wave theory are applied to analyze HS300 stock index time series. The results show these theories and methods can explain and forecast the fluctuation of financial market and provide important theoretical and empirical basis for nonlinear modeling and forecasting of financial time series.
引文
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