基于小波包与最小二乘支持向量机的时间序列预测研究
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摘要
时间序列预测作为时间序列预测领域及非线性时间动态复杂系统的重要组成部分,需要在随机性和不确定性的变化中总结规律,建立预测模型,从而为决策者提供有效的决策依据。本文以时间序列预测研究中时间序列变化特征的提取、预测模型的构建及模型参数的优化这三个关键方面为研究重点,提出了一种基于小波包与最小二乘支持向量机的时间序列预测新方法,并主要从以下几个方面进行了探讨与研究:
首先,系统地阐述了时间序列预测方法、小波分析及支持向量机的理论基础。分析比较了小波变换与小波包变换的优缺点,探讨了小波包在对信号特征提取时所表现出的优越性与适应性。讲解了最小二乘支持向量机推导机理,确立了基于最小二乘支持向量回归机来构建预测模型;
其次,建立了基于贝叶斯推断的小波包与最小二乘支持向量机时间序列预测模型。对时间序列进行小波包分解与重构,并将分解得到的近似序列和各细节序列分别单支重构到原级别上,对各个重构后的序列分别用最小二乘支持向量机进行训练。采用贝叶斯推断进行模型参数优化,训练并选取最优模型进行预测,合成而得到原序列的预测结果;
第三,基于所建的小波包与最小二乘支持向量机预测模型,针对标准QPSO算法的缺陷,提出了自适应调整收缩扩张因子β方法来优化模型参数,使得改进的QPSO算法的搜索能力更强、收敛速度更快,从而实现加快模型运算速率、提高预测精度的效果;
第四,对所建立的预测模型以及所提出的优化方法,分别以上证综指和美国纽约商品交易所原油价格为例,进行了实证分析,并对实验结果进行了多层次、多角度的分析与评测。分析结果表明,本文所建预测模型的运算速度与预测精度都有显著提高,并表现出很好的稳定性和适用性,具有良好的应用前景。
As an important part of nonlinear time series prediction and dynamic complex system,the methods of time series prediction sum up the law and establish prediction model in the change of randomness and uncertainty, so as to provide an effective decision basis for decision-makers. Focusing on the extraction of time series variation feature, the establishment of the prediction model and the optimization of the model parameters, a new method which based on wavelet packet and least squares support vector machines for time series prediction is proposed. This paper is mainly discussed and investigated in such aspects as follows:
Firstly, the basic theory of time series prediction method, wavelet analysis and support vector machine is elaborated. Then, the advantages and disadvantages between wavelet transform and wavelet packet transform are analyzed, and the adaptive advantage of wavelet packet in signal feature extraction is discussed. The mechanism of least squares support vector machines is interpreted, and the regression model based on least squares support vector machine is established;
Secondly, on the basis of Bayesian Inference, a time series prediction model based on wavelet packet and least squares support vector machines is established. By using wavelet packet decomposition and reconstruction, the time series are decomposed into the approximate sequence and the details sequences, and then reconstructed to the original single level. Separately, the reconstructed sequences are trained and predicted via LSSVM prediction model. By using Bayesian Inference, the model parameters are optimized, and the optimal model is selected to predict. The final prediction result of the original time series is the composition of the respective predictions;
Thirdly, According to WP-LSSVM prediction model, and the defect of standard QPSO algorithm, a new method which adjusting the factorβadaptively to optimize the model parameters is proposed. This proposed method makes the search ability of QPSO algorithm more effective, and the convergence faster, so as to improve the prediction accuracy of the results;
Fourthly, the proposed method is applied in the Shanghai stock index and the New York Mercantile Exchange crude oil prices respectively, and the experimental results are analyzed and evaluated completely, which shows that the computational speed and prediction accuracy are improved significantly. Above all, the proposed method shows good stability and applicability, which will perform a good prospect.
首先,系统地阐述了时间序列预测方法、小波分析及支持向量机的理论基础。分析比较了小波变换与小波包变换的优缺点,探讨了小波包在对信号特征提取时所表现出的优越性与适应性。讲解了最小二乘支持向量机推导机理,确立了基于最小二乘支持向量回归机来构建预测模型;
其次,建立了基于贝叶斯推断的小波包与最小二乘支持向量机时间序列预测模型。对时间序列进行小波包分解与重构,并将分解得到的近似序列和各细节序列分别单支重构到原级别上,对各个重构后的序列分别用最小二乘支持向量机进行训练。采用贝叶斯推断进行模型参数优化,训练并选取最优模型进行预测,合成而得到原序列的预测结果;
第三,基于所建的小波包与最小二乘支持向量机预测模型,针对标准QPSO算法的缺陷,提出了自适应调整收缩扩张因子β方法来优化模型参数,使得改进的QPSO算法的搜索能力更强、收敛速度更快,从而实现加快模型运算速率、提高预测精度的效果;
第四,对所建立的预测模型以及所提出的优化方法,分别以上证综指和美国纽约商品交易所原油价格为例,进行了实证分析,并对实验结果进行了多层次、多角度的分析与评测。分析结果表明,本文所建预测模型的运算速度与预测精度都有显著提高,并表现出很好的稳定性和适用性,具有良好的应用前景。
As an important part of nonlinear time series prediction and dynamic complex system,the methods of time series prediction sum up the law and establish prediction model in the change of randomness and uncertainty, so as to provide an effective decision basis for decision-makers. Focusing on the extraction of time series variation feature, the establishment of the prediction model and the optimization of the model parameters, a new method which based on wavelet packet and least squares support vector machines for time series prediction is proposed. This paper is mainly discussed and investigated in such aspects as follows:
Firstly, the basic theory of time series prediction method, wavelet analysis and support vector machine is elaborated. Then, the advantages and disadvantages between wavelet transform and wavelet packet transform are analyzed, and the adaptive advantage of wavelet packet in signal feature extraction is discussed. The mechanism of least squares support vector machines is interpreted, and the regression model based on least squares support vector machine is established;
Secondly, on the basis of Bayesian Inference, a time series prediction model based on wavelet packet and least squares support vector machines is established. By using wavelet packet decomposition and reconstruction, the time series are decomposed into the approximate sequence and the details sequences, and then reconstructed to the original single level. Separately, the reconstructed sequences are trained and predicted via LSSVM prediction model. By using Bayesian Inference, the model parameters are optimized, and the optimal model is selected to predict. The final prediction result of the original time series is the composition of the respective predictions;
Thirdly, According to WP-LSSVM prediction model, and the defect of standard QPSO algorithm, a new method which adjusting the factorβadaptively to optimize the model parameters is proposed. This proposed method makes the search ability of QPSO algorithm more effective, and the convergence faster, so as to improve the prediction accuracy of the results;
Fourthly, the proposed method is applied in the Shanghai stock index and the New York Mercantile Exchange crude oil prices respectively, and the experimental results are analyzed and evaluated completely, which shows that the computational speed and prediction accuracy are improved significantly. Above all, the proposed method shows good stability and applicability, which will perform a good prospect.
引文
[1]安鸿志.非线性时间训练分析.上海科学技术出版社,1998.
[2]田铮.时间序列的理论与方法.北京:高等教育出版社,2001.
[3]关履泰.小波方法与应用.北京:高等教育出版社,2007.
[4]杨福生.小波变换的工程分析与应用.北京:科学出版社,1999.
[5]张德丰.MATLAB小波分析[M].北京:机械工业出版社,2009.
[6]金得宝.基于支持向量机的股市预测研究.浙江:浙江大学,2010.
[7]刘涵,刘丁.基于最小二乘支持向量机的天然气负荷预测[J].化工学报, 2004,55(5):829-832.
[8]徐建华,李衍达.支持向量机的新方法.控制与决策,2004,19(5),480-483.
[9]刘立霞,马军海.基于LS-SVM的石油期货价格预测研究[J].计算机工程与应用,2008,44(5):230-231.
[10]崔万照,朱长纯.混沌时间序列的支持向量机预测[J].物理学报,2004,32.
[11]刘月东,韩锐,翟景春.非线性科学中的混沌.海军航空工程学院学报[J], 2007,1:177-180
[12]赵学智.小波神经网络的参数初始化研究.华南理工大学学报,2003,31(5).
[13]胡寿松,张正道.基于神经网络的非线性时间序列故障预报[J].自动化学报, 2007,7:744-748.
[14]刘建春,王正欧.一种小波神经网络的快速学习算法及其应用.天津大学学报,2003,21: 129-132.
[15]陈顺财.基于支持向量机的时间序列预测研究: [硕士学位论文].兰州:兰州理工大学,2008.
[16]程正兴.小波分析算法与应用.西安:西安交通大学出版社,1998:144-147.
[17]崔建国,李一波等.基于小波包与支持向量机的复杂信号模式识别[J].数据采集与处理.2008,23(2):123-132.
[18]孟凡龙.基于小波包和支持向量机的碰摩故障识别方法的研究: [硕士学位论文].沈阳:沈阳航空工业学院,2010.
[19]彭璐.支持向量机分类算法研究与应用[D].湖南大学,2007,3.
[20]张学工.关于统计学习理论与支持向量机.自动化学报,2000,26:134-145.
[21]曲文龙.基于支持向量机的复杂时间序列预测研究.计算机工程,2005,22.
[22]张万宏.非平稳时间序列的预测方法研究: [硕士学位论文].兰州:兰州理工大学,2007.
[23]杜贤利.基于最小二乘小波支持向量机的股票期货市场预测: [硕士学位论文].江苏:江苏大学,2008.
[24]崔万照.最小二乘小波支持向量机在非线性系统辨识中的应用[J].西安交通大学学报,2004,38(6):562-576.
[25]陈磊.基于贝叶斯最小二乘支持向量机的时用水量预测模型[J].天津大学学报, 2006,39(9):1037-1042.
[26]王欣冉,邢永丽,巨程晖.小波包与贝叶斯LS-SVM在石油价格预测中的应用[J].统计与决策.2011,33(6):162-164.
[27]李方方,赵英凯,颜昕.基于Matlab的最小二乘支持向量机的工具箱及其应用[J].计算机应用,2006,26(12):358-360.
[28]高尚,杨静宇.群智能算法及其应用[M].北京:中国水利水电出社,2006.
[29]李宁.基于粒子群的多目标优化算法.计算机工程与应用,2005,23:43-46.
[30]张春燕,须文波,孙俊等.一种具有多群体与多阶段的QPSO算法[J].计算机应用研究,2007,24(3):100-106.
[31] Vapnik V. The nature of statistical learning theory[M].NewYork: Springer- Verlag , 1995.
[32] Vapnik V. Statistical learning theory [M]. New York: Springer-Verlag, 1998.
[33] Suykens J.A.K., Vandewalle. Least squares support vector machine classifiers [J]. Neural Processing Letters, 1999, 9 (3) :293-300.
[34] Suykens J.A.K., Van Gestel T., de Moor B., et al. Least Squares Support Vector Machines [M].Singapore: World Scientific, 2002.
[35] Kwok J.T. The evidence framework applied to support vector machines [J].IEEE Transactions on Neural Network, 2000, 11(5):1162-1173.
[36] Wu Hai-shan, Chang Xiao-ling. Power load forecasting with least squares support vector machines and chaos theory[C].Proc of Intelligent Control and Automation. 2006: 4369-4373.
[37] Suykens J., Gestel T., Brabanter J.D., et al. Financial time series prediction using least squares support vector machines within the evidence framework [J].IEEE Transactions on Neural Network,2001, 12 (4) : 809-821.
[38] S.Basu,A.Mukherjee. Time series models for internet traffic. Technical Report GIT-CC-95-27,Georaia Institute of Technology,1996.
[39] Kennedy J, Eberhart R. Particle swarm optimization [C]. Proceeding IEEE International Conference on Neural Networks, 1995, 4: 1942-1948.
[40] Wen Guo, Yizheng Qiao, Haiyan Hou. BP neural network optimized with PSO algorithm and its application in forecasting. Proceedings of the IEEE international Conference on Information Acquisition. 2006:617-623.
[41] Sun Jun, Feng Bin, Xu Wen - bo.Particle swarm optimization with particles having quantum behavior [C].Proceedings of the IEEE Congress on Evolutionary Computation, 2004.
[2]田铮.时间序列的理论与方法.北京:高等教育出版社,2001.
[3]关履泰.小波方法与应用.北京:高等教育出版社,2007.
[4]杨福生.小波变换的工程分析与应用.北京:科学出版社,1999.
[5]张德丰.MATLAB小波分析[M].北京:机械工业出版社,2009.
[6]金得宝.基于支持向量机的股市预测研究.浙江:浙江大学,2010.
[7]刘涵,刘丁.基于最小二乘支持向量机的天然气负荷预测[J].化工学报, 2004,55(5):829-832.
[8]徐建华,李衍达.支持向量机的新方法.控制与决策,2004,19(5),480-483.
[9]刘立霞,马军海.基于LS-SVM的石油期货价格预测研究[J].计算机工程与应用,2008,44(5):230-231.
[10]崔万照,朱长纯.混沌时间序列的支持向量机预测[J].物理学报,2004,32.
[11]刘月东,韩锐,翟景春.非线性科学中的混沌.海军航空工程学院学报[J], 2007,1:177-180
[12]赵学智.小波神经网络的参数初始化研究.华南理工大学学报,2003,31(5).
[13]胡寿松,张正道.基于神经网络的非线性时间序列故障预报[J].自动化学报, 2007,7:744-748.
[14]刘建春,王正欧.一种小波神经网络的快速学习算法及其应用.天津大学学报,2003,21: 129-132.
[15]陈顺财.基于支持向量机的时间序列预测研究: [硕士学位论文].兰州:兰州理工大学,2008.
[16]程正兴.小波分析算法与应用.西安:西安交通大学出版社,1998:144-147.
[17]崔建国,李一波等.基于小波包与支持向量机的复杂信号模式识别[J].数据采集与处理.2008,23(2):123-132.
[18]孟凡龙.基于小波包和支持向量机的碰摩故障识别方法的研究: [硕士学位论文].沈阳:沈阳航空工业学院,2010.
[19]彭璐.支持向量机分类算法研究与应用[D].湖南大学,2007,3.
[20]张学工.关于统计学习理论与支持向量机.自动化学报,2000,26:134-145.
[21]曲文龙.基于支持向量机的复杂时间序列预测研究.计算机工程,2005,22.
[22]张万宏.非平稳时间序列的预测方法研究: [硕士学位论文].兰州:兰州理工大学,2007.
[23]杜贤利.基于最小二乘小波支持向量机的股票期货市场预测: [硕士学位论文].江苏:江苏大学,2008.
[24]崔万照.最小二乘小波支持向量机在非线性系统辨识中的应用[J].西安交通大学学报,2004,38(6):562-576.
[25]陈磊.基于贝叶斯最小二乘支持向量机的时用水量预测模型[J].天津大学学报, 2006,39(9):1037-1042.
[26]王欣冉,邢永丽,巨程晖.小波包与贝叶斯LS-SVM在石油价格预测中的应用[J].统计与决策.2011,33(6):162-164.
[27]李方方,赵英凯,颜昕.基于Matlab的最小二乘支持向量机的工具箱及其应用[J].计算机应用,2006,26(12):358-360.
[28]高尚,杨静宇.群智能算法及其应用[M].北京:中国水利水电出社,2006.
[29]李宁.基于粒子群的多目标优化算法.计算机工程与应用,2005,23:43-46.
[30]张春燕,须文波,孙俊等.一种具有多群体与多阶段的QPSO算法[J].计算机应用研究,2007,24(3):100-106.
[31] Vapnik V. The nature of statistical learning theory[M].NewYork: Springer- Verlag , 1995.
[32] Vapnik V. Statistical learning theory [M]. New York: Springer-Verlag, 1998.
[33] Suykens J.A.K., Vandewalle. Least squares support vector machine classifiers [J]. Neural Processing Letters, 1999, 9 (3) :293-300.
[34] Suykens J.A.K., Van Gestel T., de Moor B., et al. Least Squares Support Vector Machines [M].Singapore: World Scientific, 2002.
[35] Kwok J.T. The evidence framework applied to support vector machines [J].IEEE Transactions on Neural Network, 2000, 11(5):1162-1173.
[36] Wu Hai-shan, Chang Xiao-ling. Power load forecasting with least squares support vector machines and chaos theory[C].Proc of Intelligent Control and Automation. 2006: 4369-4373.
[37] Suykens J., Gestel T., Brabanter J.D., et al. Financial time series prediction using least squares support vector machines within the evidence framework [J].IEEE Transactions on Neural Network,2001, 12 (4) : 809-821.
[38] S.Basu,A.Mukherjee. Time series models for internet traffic. Technical Report GIT-CC-95-27,Georaia Institute of Technology,1996.
[39] Kennedy J, Eberhart R. Particle swarm optimization [C]. Proceeding IEEE International Conference on Neural Networks, 1995, 4: 1942-1948.
[40] Wen Guo, Yizheng Qiao, Haiyan Hou. BP neural network optimized with PSO algorithm and its application in forecasting. Proceedings of the IEEE international Conference on Information Acquisition. 2006:617-623.
[41] Sun Jun, Feng Bin, Xu Wen - bo.Particle swarm optimization with particles having quantum behavior [C].Proceedings of the IEEE Congress on Evolutionary Computation, 2004.