小波网络建模预报方法研究及其在股市预测中的应用
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摘要
股票市场是投资者、管理者和经济管理学者共同关注的热点，自19世纪股票市场建立以来，对股票价格预测模型的研究一直是众多学者关注的焦点。线性统计预测模型曾广泛应用于该领域，如AR、ARIMA模型等，但效果都不是很理想。近年来，众多学者把股票市场看作是一个非线性的确定性动力学系统，用非线性确定系统规律研究股价的行为越来越显示出强大生命力。随着非线性理论和人工智能技术的发展，小波分析和小波网络等成为金融市场强有力的分析和预测工具。
本文对小波网络预测模型进行了深入分析和研究，构建了适应于股价分析的时间序列短期预测模型。本文研究的重点是小波网络预测方法的应用和实现。主要工作如下：
从小波网络构造理论出发，对目前广泛应用的小波网络三种典型结构进行了深入分析。考虑网络算法、逼近细节能力、包含频域信息广等方面因素，指出了用RBF-WNN(以尺度函数为激励函数的小波网络)、MLP-WNN(以小波函数为激励函数的小波网络)对股票市场进行建模的不足，提出多分辨小波网络(MRA-WNN)适合股价非线性时间序列预测。应用MRA-WNN既能逼近股票市场的整体变化趋势(轮廓)，亦能捕捉变化的细节。
利用相空间重构技术，得到状态矢量作为MRA-WNN的多维输入，构建了多维MRA-WNN预测模型，并首次应用于股价时序预测，给出了实现方法。针对MRA-WNN提出了BP和多分辨率学习组合算法，解决了传统学习算法网络隐层节点数难以确定问题，克服了BP网络单尺度学习算法很难学习复杂的时间序列的不足。以深证综合指数为例，分别采用具有相同结构的MRA-WNN和RBF-WNN预测模型对股价时序进行预测，仿真结果表明，MRA-WNN具有较高的预测精度。
本文还从另一角度研究了小波分析与神经网络的结合，提出了基于小波
哈尔滨工程大学博士学位论文
分解与重构的神经网络预测方法，给出了具体实现过程。通过小波分解与
重构，把原始价格时间序列分解为规律相对简单、不同频率范围内的子波
动序列来提高神经网络的预测精度，实现了对特征不同的信号选取不同的
参数模型进行预测。通过对深证综合指数的预测，该方法比直接利用价格
波动序列预测的单一神经网络模型预测精度高。该方法可以应用到某些非
线性时间序列的预测，具有一定的推广价值。
关键词:多分辨分析;神经网络;小波网络;多分辨小波网络:
相空间重构;股市预测
Stock market is a hotspot that investors, administrators and economist pay attention to. Many academicians have focused on the research of stock market forecasting model since 19B.C. since the stock market was established. The linear statistical forecasting models, such as AR and ARIMA, have been applied in this area widely, but have not had ideal effect. In recently years, many academicians have regarded stock market as a nonlinear deterministic kinetic system. Using great the rules of nonlinear deterministic system to study the stock price shows more and more vitality. Along with the development of nonlinear theory and artificial intelligence, wavelet analysis and wavelet network become cogent tools for money market analysis and forecasting.This paper does deeply research on the wavelet network and establishes a short term prediction model which serves the time series analysis of stock price. The main research is the application and realization of the wavelet network prediction. The main work is as the following:From the configuration theory of wavelet network, this paper deeply analyses the three typical structures widely used now. Considering the factors such as the network algorithm, approaching ability and the numerous information in frequency domain, this paper points out the disadvantages of the models based RBF-WNN (wavelet network with scale function as energizing function) and MLP-WNN (wavelet network with wavelet function as energizing function), brings up a multi-resolution analysis of wavelet network (MRA-WNN) so as to realize the nonlinear time series prediction of stock price. Using MRA-WNN, we can approach the whole developing trend of the stock market (the contour), and also capture the changing details.Using the method of phase space reconstruction, we get the state vector and
regard it as the multidimensional input of MRA-WNN. Then, this text establishes multidimensional prediction MRA-WNN model, and apples it on the prediction of stock price time series for the first time. Otherwise, it gives a realization method. Based on MRA-WNN, this paper brings up an algorithm of BP combined with multi-resolution analysis, which resolves the problems that are uncertain note numbers of the hidden layer for traditional training algorithm and are difficult to study complex time series by the single-scale algorithm of BP network. Taking Shenzheng's integrated index for example, this paper forecasts the stock price time series using the MRA-WNN and RBF-WNN model with the same structure respectively. The simulation result indicates that the MAR-WNN has a high prediction precision.On the other hand, this paper does research on the combination of wavelet analysis and neural network and brings up a neural network prediction method and its concrete realization process based wavelet decomposition and reconstruction. Through this method, this paper decomposed the price function into a series of wavelets in different frequency range, whose fluctuation rule can be easily grasped. This method increases the neural network prediction precision, and makes it possible to predict signals with different characteristics with prediction models of different parameters. The prediction of Shenzheng's integrative index indicates that this method is more accurate than the single neural network prediction model which directly used the series of price fluctuation to predict, and can be widely used in some nonlinear time series prediction.
本文对小波网络预测模型进行了深入分析和研究，构建了适应于股价分析的时间序列短期预测模型。本文研究的重点是小波网络预测方法的应用和实现。主要工作如下：
从小波网络构造理论出发，对目前广泛应用的小波网络三种典型结构进行了深入分析。考虑网络算法、逼近细节能力、包含频域信息广等方面因素，指出了用RBF-WNN(以尺度函数为激励函数的小波网络)、MLP-WNN(以小波函数为激励函数的小波网络)对股票市场进行建模的不足，提出多分辨小波网络(MRA-WNN)适合股价非线性时间序列预测。应用MRA-WNN既能逼近股票市场的整体变化趋势(轮廓)，亦能捕捉变化的细节。
利用相空间重构技术，得到状态矢量作为MRA-WNN的多维输入，构建了多维MRA-WNN预测模型，并首次应用于股价时序预测，给出了实现方法。针对MRA-WNN提出了BP和多分辨率学习组合算法，解决了传统学习算法网络隐层节点数难以确定问题，克服了BP网络单尺度学习算法很难学习复杂的时间序列的不足。以深证综合指数为例，分别采用具有相同结构的MRA-WNN和RBF-WNN预测模型对股价时序进行预测，仿真结果表明，MRA-WNN具有较高的预测精度。
本文还从另一角度研究了小波分析与神经网络的结合，提出了基于小波
哈尔滨工程大学博士学位论文
分解与重构的神经网络预测方法，给出了具体实现过程。通过小波分解与
重构，把原始价格时间序列分解为规律相对简单、不同频率范围内的子波
动序列来提高神经网络的预测精度，实现了对特征不同的信号选取不同的
参数模型进行预测。通过对深证综合指数的预测，该方法比直接利用价格
波动序列预测的单一神经网络模型预测精度高。该方法可以应用到某些非
线性时间序列的预测，具有一定的推广价值。
关键词:多分辨分析;神经网络;小波网络;多分辨小波网络:
相空间重构;股市预测
Stock market is a hotspot that investors, administrators and economist pay attention to. Many academicians have focused on the research of stock market forecasting model since 19B.C. since the stock market was established. The linear statistical forecasting models, such as AR and ARIMA, have been applied in this area widely, but have not had ideal effect. In recently years, many academicians have regarded stock market as a nonlinear deterministic kinetic system. Using great the rules of nonlinear deterministic system to study the stock price shows more and more vitality. Along with the development of nonlinear theory and artificial intelligence, wavelet analysis and wavelet network become cogent tools for money market analysis and forecasting.This paper does deeply research on the wavelet network and establishes a short term prediction model which serves the time series analysis of stock price. The main research is the application and realization of the wavelet network prediction. The main work is as the following:From the configuration theory of wavelet network, this paper deeply analyses the three typical structures widely used now. Considering the factors such as the network algorithm, approaching ability and the numerous information in frequency domain, this paper points out the disadvantages of the models based RBF-WNN (wavelet network with scale function as energizing function) and MLP-WNN (wavelet network with wavelet function as energizing function), brings up a multi-resolution analysis of wavelet network (MRA-WNN) so as to realize the nonlinear time series prediction of stock price. Using MRA-WNN, we can approach the whole developing trend of the stock market (the contour), and also capture the changing details.Using the method of phase space reconstruction, we get the state vector and
regard it as the multidimensional input of MRA-WNN. Then, this text establishes multidimensional prediction MRA-WNN model, and apples it on the prediction of stock price time series for the first time. Otherwise, it gives a realization method. Based on MRA-WNN, this paper brings up an algorithm of BP combined with multi-resolution analysis, which resolves the problems that are uncertain note numbers of the hidden layer for traditional training algorithm and are difficult to study complex time series by the single-scale algorithm of BP network. Taking Shenzheng's integrated index for example, this paper forecasts the stock price time series using the MRA-WNN and RBF-WNN model with the same structure respectively. The simulation result indicates that the MAR-WNN has a high prediction precision.On the other hand, this paper does research on the combination of wavelet analysis and neural network and brings up a neural network prediction method and its concrete realization process based wavelet decomposition and reconstruction. Through this method, this paper decomposed the price function into a series of wavelets in different frequency range, whose fluctuation rule can be easily grasped. This method increases the neural network prediction precision, and makes it possible to predict signals with different characteristics with prediction models of different parameters. The prediction of Shenzheng's integrative index indicates that this method is more accurate than the single neural network prediction model which directly used the series of price fluctuation to predict, and can be widely used in some nonlinear time series prediction.
引文
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