鲁棒自适应BP算法及其在股票价格预测中的应用
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摘要
本文从基本BP算法在应用中存在的不足出发，着重分析了训练样本中所含噪声对基本BP算法在网络训练过程中产生的不良影响，并以此为依据，采用鲁棒统计技术，同时在优化算法上做了一些有益的改进，提出一种新的具有较强抗干扰能力的BP算法——鲁棒自适应BP算法，并将其应用于动态BP网络，进行股票价格的预测，取得了较好的预测效果。
与基本BP算法相比，本文提出的鲁棒自适应BP算法具有以下优点：(1) 与鲁棒统计技术相结合，通过训练样本相对偏差的大小，确定不同训练样本对能量函数的贡献，来抑制含高噪声干扰样本对网络训练的不良影响，从而增强训练的鲁棒性，提高网络训练的收敛速度；(2) 采用相对偏差和绝对偏差两种偏差形式对权值进行调整，提高了网络的训练精度； (3)在采用梯度下降算法对权值进行调整的基础上，通过将学习速率设为训练误差及误差梯度的特殊函数，使学习速率依赖于网络训练时误差瞬时的变化而自适应的改变，从而可以克服基本BP算法容易陷入局部极小区域的弊端，使训练过程能够很快的“跳出”局部极小区域而达到全局最优。
大量仿真结果表明，本文提出的鲁棒自适应BP算法在收敛速度，收敛精度，尤其是抗噪声干扰的能力上比其他BP算法具有更好的优势。
算法的应用上，本文根据股票市场具有高噪声，高度非线性，难于精确建模等特点，将提出的鲁棒自适应BP算法应用于动态BP网络中进行股票价格的预测，一方面通过动态BP网络实现了无需精确建模而得到系统良好特性的效果，另一方面发挥了本算法鲁棒性强的优势，克服了训练样本中高噪声对网络训练的影响，从而得到较好的预测结果。
Based upon the deficiencies of the Back Propagation Algorithm in the practical application, after some mechanisms effecting the network training and the other performances are analyzed when training samples with disturbance are employed in training, in this paper, through combining the chief thoughts of the classical BP algorithm and the robust statistic technique, improving the optimal algorithm of the BP algorithm, A new algorithm with high robustness-Robust Adaptive BP algorithm is proposed, and also make a good effect when integrated this new algorithm with the dynamical BP network to predict the stock price.
Compared with the classical BP algorithm, robust adaptive BP algorithm possesses some advantages as following:(1) Increasing the accuracy of the network training by means of using both the relative and absolute residual to adjust the weight values;(2) Improve the robustness and the network convergence rate through combining with the robust statistic technique by way of judging the values of the samples' relative residual to establish the energy function so that can suppress the effect on network training because of the samples with high noise disturbances;(3)Prevent entrapping into the local minima area and obtain the global optimal result owing to setting the learning rate to be the function of the errors and the error gradients when network is trained. The learning rate of the weights update change with the error values of the network adaptively so that can easily get rid of the disadvantage of the classical BP algorithm that is liable to entrap into the local minima areas.
The simulation results of the new algorithm show that the robust adaptive BP algorithm is more efficient than others on the convergent rate, accuracy and especially on resisting to the noise effects.
According to the characters of the stock market that possesses kinds of noises, serious nonlinear and difficult to model a precise mathematical equation, in this paper, applying the robust adaptive BP algorithm into the dynamical BP network to predict the stock price, one side can realize the course of having no use of modeling the accuracy model to the stock systems, and on the other hand can make good use of the strong robustness of the new algorithm result in conquer the influence of the noises to the network training and achieve the better prediction results.
与基本BP算法相比，本文提出的鲁棒自适应BP算法具有以下优点：(1) 与鲁棒统计技术相结合，通过训练样本相对偏差的大小，确定不同训练样本对能量函数的贡献，来抑制含高噪声干扰样本对网络训练的不良影响，从而增强训练的鲁棒性，提高网络训练的收敛速度；(2) 采用相对偏差和绝对偏差两种偏差形式对权值进行调整，提高了网络的训练精度； (3)在采用梯度下降算法对权值进行调整的基础上，通过将学习速率设为训练误差及误差梯度的特殊函数，使学习速率依赖于网络训练时误差瞬时的变化而自适应的改变，从而可以克服基本BP算法容易陷入局部极小区域的弊端，使训练过程能够很快的“跳出”局部极小区域而达到全局最优。
大量仿真结果表明，本文提出的鲁棒自适应BP算法在收敛速度，收敛精度，尤其是抗噪声干扰的能力上比其他BP算法具有更好的优势。
算法的应用上，本文根据股票市场具有高噪声，高度非线性，难于精确建模等特点，将提出的鲁棒自适应BP算法应用于动态BP网络中进行股票价格的预测，一方面通过动态BP网络实现了无需精确建模而得到系统良好特性的效果，另一方面发挥了本算法鲁棒性强的优势，克服了训练样本中高噪声对网络训练的影响，从而得到较好的预测结果。
Based upon the deficiencies of the Back Propagation Algorithm in the practical application, after some mechanisms effecting the network training and the other performances are analyzed when training samples with disturbance are employed in training, in this paper, through combining the chief thoughts of the classical BP algorithm and the robust statistic technique, improving the optimal algorithm of the BP algorithm, A new algorithm with high robustness-Robust Adaptive BP algorithm is proposed, and also make a good effect when integrated this new algorithm with the dynamical BP network to predict the stock price.
Compared with the classical BP algorithm, robust adaptive BP algorithm possesses some advantages as following:(1) Increasing the accuracy of the network training by means of using both the relative and absolute residual to adjust the weight values;(2) Improve the robustness and the network convergence rate through combining with the robust statistic technique by way of judging the values of the samples' relative residual to establish the energy function so that can suppress the effect on network training because of the samples with high noise disturbances;(3)Prevent entrapping into the local minima area and obtain the global optimal result owing to setting the learning rate to be the function of the errors and the error gradients when network is trained. The learning rate of the weights update change with the error values of the network adaptively so that can easily get rid of the disadvantage of the classical BP algorithm that is liable to entrap into the local minima areas.
The simulation results of the new algorithm show that the robust adaptive BP algorithm is more efficient than others on the convergent rate, accuracy and especially on resisting to the noise effects.
According to the characters of the stock market that possesses kinds of noises, serious nonlinear and difficult to model a precise mathematical equation, in this paper, applying the robust adaptive BP algorithm into the dynamical BP network to predict the stock price, one side can realize the course of having no use of modeling the accuracy model to the stock systems, and on the other hand can make good use of the strong robustness of the new algorithm result in conquer the influence of the noises to the network training and achieve the better prediction results.
引文
1 焦李成. 神经网络计算. 西安电子科技大学出版社, 1993:2~5
2 王永骥，涂健. 神经元网络控制. 机械工业出版社, 1998:14~17
3 刘豹,胡代平. 神经网络在预测中的一些应用研究. 系统工程学报, 1999，14(4):338~344
4 F.R.Hampel, P.J.Rousseeuw, E.M.Ronchetti and W.A.Stahel. Robust Statistics—The Approach Based on Influence Function. New York:Wiley, 1986:150~177
5 陈国良,韩文廷. 人工神经网络理论研究进展. 电子学报, 1996，24(1):70~75
6 刘永红. 神经网络理论的发展与前沿问题. 信息与控制,1999,28(1):31~46
7 王科俊, 王克成. 神经网络建模、预报与控制. 哈尔滨工程大学出版社, 1996：1~3
8 J.Hertz. Introduction to the Theory of Neural Computation. Addison-Wesley Publish Company. 1991:1~12
9 汪镭, 周国兴, 吴启迪. 人工神经网络理论在控制领域中的应用综述. 同济大学学报, 2001,29(3):357~361
10 K.J. Hunt. Neural Network for Control Systems－A Survey. Automatic, 1992,28
(6):1083~1112
11 黄小原. 金融工程:信息与控制领域的挑战. 信息与控制 ,2001,30(2):149~154
12 郭亚军, 边旭, 郭音. 对我国当前经济预测的新思考. 数量经济技术经济研究, 1997,8:9~12
13 杭行. 股票投资. 河北人民出版社, 1999:12~55
14 杨书郎. 关于股票风险控制的某些问题的研究. 厦门大学学报（自然科学版）, 1998,37(1):24~27
15 E.W.Saad, D.V.Prokhorov and D.C.Wunsch. Comparative Study of Stock Trend
Prediction Using Time Delay, Recurrent and Probabilistic Neural Networks. IEEE Trans.on Neural Networks.1998,9(6):1456~1470
16 XieZhongjie, Wong Heung and Liu Yali. Artificial Neuron Network and Its Application to Financial Forecasting. Acta Scientiarum Naturalium Universitatis Pekingensis. 2001,37(3):421~425
17 张秀艳, 徐立本, 李太浩. 人工神经元网络在经济学中应用的研究现状及研发策略. 数量经济技术经济研究, 2001,5:92~94
18 刘新勇, 贺江峰, 孟祥泽, 陈增强, 袁著祉. 基于神经网络的股市预测. 南开大学学报(自然科学),1998,31(3):39~44
19 赵建, 黄炯. 基于神经网络的股市预测. 计算机研究与发展. 1996,33(9):692
~697
20 A.N.Refenes, A.Zapranis and G.Francis. Stock Performance Modeling Using Neural Networks: A Comparative Study with Regression Models. Neural Networks, 1994:7(2):375~388
21 M.Kastra. Forecasting Combining with Neural Networks.Forecast, 1996,15(1):49
~61
22 王维, 贺京同, 张建勋, 卢桂章, 张灿. 人工神经网络在非线性经济预测中的应用. 系统工程学报, 2000,15(2):202~207
23 焦李成. 神经网络系统理论.西安电子科技大学出版社,1995:9~22
24 王永骥, 涂健. 神经元网络控制机械工业出版社. 1998:7~13
25 G.W.Irwin, K.Warwick and K.J.Hunt. Neural Network Applications in Control. The Institution of Electrical Engineers, 1995:52~67
26 许东, 吴铮. 基于MATLAB6.X的系统分析与设计—神经网络. 西安电子科技大学出版社, 2002:4~5
27 David Naylor, Simon Jones and David Myers. Back propagation in linear Arrays
—A Performance Analysis and Optimization. IEEE Trans. on Neural Networks,1995,6(3):583~595
28 A.V.Vasilakos and N.H.Loukas. ANASA—A Stochastic Reinforcement Algorithm for Real-Valued Neural Computation. IEEE Trans. on Neural Networks, 1996，7(4):830~842
29 A.G.Parlos. An Accelerated Learning Algorithm for Back-Propagation Neural Networks. IEEE Trans. on Neural Networks, 1994,5(3):493~497
30 V.V.Phansalkar and P.S.Sastry. Analysis of the Back-Propagation Algorithm with Momentum. IEEE Trans. on Neural Networks, 1994,5(3):505~506
31 R.S.Scalero and N.Tepedelenioglu. A Fast New Algorithm for Training Feedforward Neuarl Networks.IEEE Trans. on Signal Processing. 1992,40(2):202
~210
32 Si-Zhao Qin, Hong-Te Su and T.J.McAvoy. Comparison of Four Neural Net Learning Methods for Dynamic System Identification. IEEE Trans. on Neural Networks, 1992,3(1):122~130
33 R. Hecht-Nielsen. Theory of the Backpropagation. Proc.IEEE IJCNN,1989,1:593
~605
34 Lasse Holmstrom and Petri Koistinen. Using Additive Noise in Back-Propagation Training. IEEE Trans. on Neural Networks,1992,3(1):24~38
35 D.V.Chen and R.C.Jain. A Robust Back Propagation Learning Algorithm for Function Approximation. IEEE Trans. on Neural Networks,1994:467~479
36 B.Efron and R.Tibshirani. Bootstrap Methods for Standard Errors, Confidence Intervals and Other Measures of Statistical Accuracy. Statistic Science.1988,1(1):
54~77
37 Xiao-Hu Yu,Guo-An Chen and Shi-Xin Cheng.Dynamic Learning Rate
Optimization of the Backpropagation Algorithm. IEEE Trans. on Neural Networks, 1995,6(3):669~677
38 A.G.Parlos, B. Fernandez, J.Muthusami and Wei K.Tsai. An Accelerated Learning Algorithm for Multilayer Perception Networks. IEEE Trans.on Neural Networks, 1994,5(3):493~497
39 Y.LeCun. A Theoretical Framework for Back propagation. In Proc.1988 Connectionist Models Summer School. 1988,June:17~26
40 王永骥, 涂健. 神经元网络控制. 机械工业出版社,1998:167~170
41 田明,戴汝为.基于动态BP神经网络的系统辨识方法. 自动化学报, 1993,19(4):450~453
42 K S,Narendra and K.Parthasarathy. Identification and control of dynamical systems using neural networks. IEEE Trans. on Neural Networks, 1990,1(1):4~27
43 P.S.Sastry, G.Santharam and K.P.Unnikrishnan. Memory Neuron Networks for Identification and Control of Dynamical Systems. IEEE Trans. on Neural Networks, 1994,5(2)306~319
44 赵振全, 蒋瑛琨, 代丽, 卢世春. 我国证券市场结构分析及优化. 数量经济技术经济研究, 2001,6:36~38
45 吴微, 陈维强, 刘波. 用BP神经网络预测股票市场涨跌. 大连理工大学学报, 2001,41(1):9~15
46 www.stockstar.com 证券之星
47 www.hxinfo.com 华夏证券资讯网
48 www.f10.com.cn 中国证券在线
2 王永骥，涂健. 神经元网络控制. 机械工业出版社, 1998:14~17
3 刘豹,胡代平. 神经网络在预测中的一些应用研究. 系统工程学报, 1999，14(4):338~344
4 F.R.Hampel, P.J.Rousseeuw, E.M.Ronchetti and W.A.Stahel. Robust Statistics—The Approach Based on Influence Function. New York:Wiley, 1986:150~177
5 陈国良,韩文廷. 人工神经网络理论研究进展. 电子学报, 1996，24(1):70~75
6 刘永红. 神经网络理论的发展与前沿问题. 信息与控制,1999,28(1):31~46
7 王科俊, 王克成. 神经网络建模、预报与控制. 哈尔滨工程大学出版社, 1996：1~3
8 J.Hertz. Introduction to the Theory of Neural Computation. Addison-Wesley Publish Company. 1991:1~12
9 汪镭, 周国兴, 吴启迪. 人工神经网络理论在控制领域中的应用综述. 同济大学学报, 2001,29(3):357~361
10 K.J. Hunt. Neural Network for Control Systems－A Survey. Automatic, 1992,28
(6):1083~1112
11 黄小原. 金融工程:信息与控制领域的挑战. 信息与控制 ,2001,30(2):149~154
12 郭亚军, 边旭, 郭音. 对我国当前经济预测的新思考. 数量经济技术经济研究, 1997,8:9~12
13 杭行. 股票投资. 河北人民出版社, 1999:12~55
14 杨书郎. 关于股票风险控制的某些问题的研究. 厦门大学学报（自然科学版）, 1998,37(1):24~27
15 E.W.Saad, D.V.Prokhorov and D.C.Wunsch. Comparative Study of Stock Trend
Prediction Using Time Delay, Recurrent and Probabilistic Neural Networks. IEEE Trans.on Neural Networks.1998,9(6):1456~1470
16 XieZhongjie, Wong Heung and Liu Yali. Artificial Neuron Network and Its Application to Financial Forecasting. Acta Scientiarum Naturalium Universitatis Pekingensis. 2001,37(3):421~425
17 张秀艳, 徐立本, 李太浩. 人工神经元网络在经济学中应用的研究现状及研发策略. 数量经济技术经济研究, 2001,5:92~94
18 刘新勇, 贺江峰, 孟祥泽, 陈增强, 袁著祉. 基于神经网络的股市预测. 南开大学学报(自然科学),1998,31(3):39~44
19 赵建, 黄炯. 基于神经网络的股市预测. 计算机研究与发展. 1996,33(9):692
~697
20 A.N.Refenes, A.Zapranis and G.Francis. Stock Performance Modeling Using Neural Networks: A Comparative Study with Regression Models. Neural Networks, 1994:7(2):375~388
21 M.Kastra. Forecasting Combining with Neural Networks.Forecast, 1996,15(1):49
~61
22 王维, 贺京同, 张建勋, 卢桂章, 张灿. 人工神经网络在非线性经济预测中的应用. 系统工程学报, 2000,15(2):202~207
23 焦李成. 神经网络系统理论.西安电子科技大学出版社,1995:9~22
24 王永骥, 涂健. 神经元网络控制机械工业出版社. 1998:7~13
25 G.W.Irwin, K.Warwick and K.J.Hunt. Neural Network Applications in Control. The Institution of Electrical Engineers, 1995:52~67
26 许东, 吴铮. 基于MATLAB6.X的系统分析与设计—神经网络. 西安电子科技大学出版社, 2002:4~5
27 David Naylor, Simon Jones and David Myers. Back propagation in linear Arrays
—A Performance Analysis and Optimization. IEEE Trans. on Neural Networks,1995,6(3):583~595
28 A.V.Vasilakos and N.H.Loukas. ANASA—A Stochastic Reinforcement Algorithm for Real-Valued Neural Computation. IEEE Trans. on Neural Networks, 1996，7(4):830~842
29 A.G.Parlos. An Accelerated Learning Algorithm for Back-Propagation Neural Networks. IEEE Trans. on Neural Networks, 1994,5(3):493~497
30 V.V.Phansalkar and P.S.Sastry. Analysis of the Back-Propagation Algorithm with Momentum. IEEE Trans. on Neural Networks, 1994,5(3):505~506
31 R.S.Scalero and N.Tepedelenioglu. A Fast New Algorithm for Training Feedforward Neuarl Networks.IEEE Trans. on Signal Processing. 1992,40(2):202
~210
32 Si-Zhao Qin, Hong-Te Su and T.J.McAvoy. Comparison of Four Neural Net Learning Methods for Dynamic System Identification. IEEE Trans. on Neural Networks, 1992,3(1):122~130
33 R. Hecht-Nielsen. Theory of the Backpropagation. Proc.IEEE IJCNN,1989,1:593
~605
34 Lasse Holmstrom and Petri Koistinen. Using Additive Noise in Back-Propagation Training. IEEE Trans. on Neural Networks,1992,3(1):24~38
35 D.V.Chen and R.C.Jain. A Robust Back Propagation Learning Algorithm for Function Approximation. IEEE Trans. on Neural Networks,1994:467~479
36 B.Efron and R.Tibshirani. Bootstrap Methods for Standard Errors, Confidence Intervals and Other Measures of Statistical Accuracy. Statistic Science.1988,1(1):
54~77
37 Xiao-Hu Yu,Guo-An Chen and Shi-Xin Cheng.Dynamic Learning Rate
Optimization of the Backpropagation Algorithm. IEEE Trans. on Neural Networks, 1995,6(3):669~677
38 A.G.Parlos, B. Fernandez, J.Muthusami and Wei K.Tsai. An Accelerated Learning Algorithm for Multilayer Perception Networks. IEEE Trans.on Neural Networks, 1994,5(3):493~497
39 Y.LeCun. A Theoretical Framework for Back propagation. In Proc.1988 Connectionist Models Summer School. 1988,June:17~26
40 王永骥, 涂健. 神经元网络控制. 机械工业出版社,1998:167~170
41 田明,戴汝为.基于动态BP神经网络的系统辨识方法. 自动化学报, 1993,19(4):450~453
42 K S,Narendra and K.Parthasarathy. Identification and control of dynamical systems using neural networks. IEEE Trans. on Neural Networks, 1990,1(1):4~27
43 P.S.Sastry, G.Santharam and K.P.Unnikrishnan. Memory Neuron Networks for Identification and Control of Dynamical Systems. IEEE Trans. on Neural Networks, 1994,5(2)306~319
44 赵振全, 蒋瑛琨, 代丽, 卢世春. 我国证券市场结构分析及优化. 数量经济技术经济研究, 2001,6:36~38
45 吴微, 陈维强, 刘波. 用BP神经网络预测股票市场涨跌. 大连理工大学学报, 2001,41(1):9~15
46 www.stockstar.com 证券之星
47 www.hxinfo.com 华夏证券资讯网
48 www.f10.com.cn 中国证券在线
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