时间序列短期预测的方法和技术
摘要
时间序列是指按照时间顺序取得的一系列观测值,很多数据是以时间序列的形式出现的,从经济、金融到工程技术,从天文、地理到气象,从医学到生物等各个领域都涉及到时间序列,例如船舶运动,每天的气温,公路事故数量的周度序列等等。在自然科学和社会科学各研究领域中,大量决策问题都离不开预测,时间序列预测是指利用时间序列的若干历史观测值来预测未来某时刻的取值。时间序列预测的应用非常广泛,如天气预报,股价指数的预测,船舶运动的极短期预报等等。
本文第一章介绍了该课题的背景意义以及时间序列预测的国内外研究现状；在第二章中给出了五种常用的时间序列预测方法基本原理的详细说明,包括线性预测方法(自回归模型AR、自回归滑动平均模型ARMA、求和自回归滑动平均模型ARIMA)和非线性预测方法(径向基函数RBF神经网络和BP网络)。第三章论文在MATLAB环境下实现了这五种方法用于海浪信号的预测,并且比较了这些方法预测后的四种误差,包括偏差、归一化偏差、均方根误差、标准偏差。同时,比较不同情况下这些方法预测的效果,分别是：预测步长增加时；取不同的时间段进行预测时,预测误差的大小等；比较了这些方法用于均匀分布和高斯分布随机数据序列的预测效果。第四章在MATLAB的GUIDE平台上开发了一个时间序列短期预测系统,涵盖了以上五种预测方法,该系统可以方便的对时间序列进行预测,可自由选择预测方法,待预测的数据和预测步长,能直观地显示预测结果以及常用的四种误差值,便于用户对这些方法的预测效果进行评估分析。最后,第五章总结了以上五种预测方法的预测性能并对方法的改进之处寄予展望。
本文的主要贡献有：(1)在MATLAB环境下实现了五种常用的时间序列预测方法,并使用这些方法对海浪信号、均匀分布和高斯分布数据进行了短期预测。(2)比较这五种预测方法的预测步长,稳定性,预测精度和运行时间,总结了它们的优缺点。(3)在MATLAB的GUIDE平台上开发了时间序列短期预测系统,方便使用五种方法对时间序列进行预测。
Time series is a series of observations obtained according to the time order. A lot of data is in the form of time series. From the economic, finance to engineering, from astronomy, geography to meteorology, from medicine to biology, and so on. All of these areas are related to time-series. For example, ship motion, the daily temperature, and the sequence weekly of the number of road accidents and so on. In the research fields of natural sciences and social sciences, a large number of decision-making can not be separated from prediction. Time series forecasting refers to the use of the historical observations of time series to predict the value at a future time. Time series forecasting is widely used, such as the weather forecasts, stock price index forecasts, extremely short-time prediction of ship motion and so on.
In chapter 1 this paper introduces the research background of time series forecasting and the status at home and abroad. Chapter 2 presents detailed description of the basic theories on the five kinds of commonly used time series forecasting methods, including the linear forecasting methods (auto-regressive model AR, auto-regressive moving average model ARMA, and integrated autoregressive moving average model ARIMA) and the non-linear forecasting methods (radial basis function RBF neural network and BP network). In chapter 3, firstly, we implement these five kinds of methods for forecasting a wave signal, and experimentally compare the four kinds of error on these five forecasting methods, including bias, normalized bias, root mean square error and standard deviation. Furthermore, we compare the forecasting performances of these methods in different circumstances. Namely, when the prediction step increases, when take a different time period for forecasting, the magnitude of error for these five methods. Finally, we compare their performance on forecasting of the Uniform distribution and Gaussian distribution random sequence. In chapter 4, we develop a time series short-term forecasting system in the MATLAB GUIDE development platform, it covers the five kinds of forecasting methods above and we can easily predict time series on it. We are free to choose forecasting methods, data for forecasting and the prediction step, then the system can visually indicate the forecasting results and four kinds of error commonly used, it helps us in assessment and analysis of these forecasting methods. Finally, Chapter 5 summarizes the performances of these five forecasting methods and gives an outlook for their improvements.
The main contributions of this paper are:(1) five kinds of time series forecasting methods are implemented in the MATLAB environment, and these methods are used on the short-term prediction on a wave signal and sequences satisfies Uniform distribution and Gaussian distribution. (2) make a comparison to the prediction steps, stability, prediction accuracy and running time of the five forecasting methods, summarize their advantages and disadvantages. (3) develop a short-term time series forecasting system in the MATLAB GUIDE development platform, easily use the five forecasting methods for time series forecasting.
本文第一章介绍了该课题的背景意义以及时间序列预测的国内外研究现状；在第二章中给出了五种常用的时间序列预测方法基本原理的详细说明,包括线性预测方法(自回归模型AR、自回归滑动平均模型ARMA、求和自回归滑动平均模型ARIMA)和非线性预测方法(径向基函数RBF神经网络和BP网络)。第三章论文在MATLAB环境下实现了这五种方法用于海浪信号的预测,并且比较了这些方法预测后的四种误差,包括偏差、归一化偏差、均方根误差、标准偏差。同时,比较不同情况下这些方法预测的效果,分别是：预测步长增加时；取不同的时间段进行预测时,预测误差的大小等；比较了这些方法用于均匀分布和高斯分布随机数据序列的预测效果。第四章在MATLAB的GUIDE平台上开发了一个时间序列短期预测系统,涵盖了以上五种预测方法,该系统可以方便的对时间序列进行预测,可自由选择预测方法,待预测的数据和预测步长,能直观地显示预测结果以及常用的四种误差值,便于用户对这些方法的预测效果进行评估分析。最后,第五章总结了以上五种预测方法的预测性能并对方法的改进之处寄予展望。
本文的主要贡献有：(1)在MATLAB环境下实现了五种常用的时间序列预测方法,并使用这些方法对海浪信号、均匀分布和高斯分布数据进行了短期预测。(2)比较这五种预测方法的预测步长,稳定性,预测精度和运行时间,总结了它们的优缺点。(3)在MATLAB的GUIDE平台上开发了时间序列短期预测系统,方便使用五种方法对时间序列进行预测。
Time series is a series of observations obtained according to the time order. A lot of data is in the form of time series. From the economic, finance to engineering, from astronomy, geography to meteorology, from medicine to biology, and so on. All of these areas are related to time-series. For example, ship motion, the daily temperature, and the sequence weekly of the number of road accidents and so on. In the research fields of natural sciences and social sciences, a large number of decision-making can not be separated from prediction. Time series forecasting refers to the use of the historical observations of time series to predict the value at a future time. Time series forecasting is widely used, such as the weather forecasts, stock price index forecasts, extremely short-time prediction of ship motion and so on.
In chapter 1 this paper introduces the research background of time series forecasting and the status at home and abroad. Chapter 2 presents detailed description of the basic theories on the five kinds of commonly used time series forecasting methods, including the linear forecasting methods (auto-regressive model AR, auto-regressive moving average model ARMA, and integrated autoregressive moving average model ARIMA) and the non-linear forecasting methods (radial basis function RBF neural network and BP network). In chapter 3, firstly, we implement these five kinds of methods for forecasting a wave signal, and experimentally compare the four kinds of error on these five forecasting methods, including bias, normalized bias, root mean square error and standard deviation. Furthermore, we compare the forecasting performances of these methods in different circumstances. Namely, when the prediction step increases, when take a different time period for forecasting, the magnitude of error for these five methods. Finally, we compare their performance on forecasting of the Uniform distribution and Gaussian distribution random sequence. In chapter 4, we develop a time series short-term forecasting system in the MATLAB GUIDE development platform, it covers the five kinds of forecasting methods above and we can easily predict time series on it. We are free to choose forecasting methods, data for forecasting and the prediction step, then the system can visually indicate the forecasting results and four kinds of error commonly used, it helps us in assessment and analysis of these forecasting methods. Finally, Chapter 5 summarizes the performances of these five forecasting methods and gives an outlook for their improvements.
The main contributions of this paper are:(1) five kinds of time series forecasting methods are implemented in the MATLAB environment, and these methods are used on the short-term prediction on a wave signal and sequences satisfies Uniform distribution and Gaussian distribution. (2) make a comparison to the prediction steps, stability, prediction accuracy and running time of the five forecasting methods, summarize their advantages and disadvantages. (3) develop a short-term time series forecasting system in the MATLAB GUIDE development platform, easily use the five forecasting methods for time series forecasting.
引文
[1]G. E. P. Box, G. M. Jenkins, G. C. Reinsel,时间序列分析：预测与控制,中国统计出版社,1999.
[2]安鸿志,陈兆国,杜金观,潘一民.时间序列的分析与应用[M].北京：科学出版社,1983
[3]杨叔子,吴雅,轩建平等.时间序列分析的工程应用[M].武汉：华中科技大学出版社,2007.
[4]袁振洲.应用自回归积分移动平均法预测铁路货源货流发展趋势.铁道学报.1996年4月
[5]David E. Rumelhart, James L. McClelland. Parallel Distributed Processing: Exploration in the Microstructure of Cognition. Cambridge:MIT Press,1986.
[6]Lapedes. A, Faber. R. Non-linear Signal Processing Using Neural Networks: Prediction and System Modeling. Los Alamos National Laboratory Report,1987
[7]J. Moody, C. Darken. Fast learning in networks of locally-tuned processing units. Neural Computation,1989, (1):281-294.
[8]Leonard Studer, Francesco Masulli. Building a neuro-fuzzy system to efficiently forecast chaotic time series[J]. Nuclear Instruments and Methods in Physics Research A 389(1997) 264-267.
[9]Roman Rosipal, Milos Koska, Igor Farkas. Prediction of chaotic time-series with a resource-allocating RBF network[J]. Neural Processing Letters 7:185-197,1998.
[10]杨红卫,何晨.基于人工神经网络的毫米波雨衰减预测.上海交通大学学报.2001,35(1)：13-16.
[11]吴微,陈维强.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.
[12]周德懋,李舟军,康荣雷.基于时间序列分析的网络流量预测模型研究.现代电子技术,2009年第8期.
[13]周惠,时间序列预测方法在港口行业中的应用.中国农业大学硕士学位论文.2004.
[14]杨建萍.基于ARIMA模型的用电量时间序列建模和预报.工程数学学报,25(4),2008.
[15]张利,基于时间序列ARIMA模型的分析预测算法研究及系统实现.江苏 大学硕士学位论文,2008.
[16]S.M.潘迪斯,吴宪民.时间序列及系统分析与应用[M].北京：机械工业出版社,1988
[17]张树京,齐立心.时间序列分析简明教程.清华大学出版社,北方交通大学出版社,2003.
[18]王燕.应用时间序列分析.中国人民大学出版社,2005.
[19]朱文谱,郜焕秋,谢楠等.船舶运动自适应TAR模型预报方法.中国船舶科学研究中心技术报告,1997.
[20]Holger R. Maier, Graeme C. Dandy. Neural networks for the prediction and forecasting of water resources variables:a review of modeling issues and applications. Environmental Modelling & Software 15(2000) 101-124.1999.
[21]I. A. Basheer, M. Hajmeer. Artificial neural networks:fundamentals, computing, design, and application. Journal of Microbiological Methods 43(2000) 3-31,2000.
[22]Donald F. Specht. A General Regression Neural Network. IEEE Transaction on Neural Networks Vol.2. No.6. November,1991.
[23]D. C. Park, M. A. El-Sharkawi, R. J. Marks Ⅱ, et al. Electric load forecasting using an artificial neural network. IEEE Transaction on Power Systems, Vol.6, No.2, May 1991.
[24]A. A. Khan, K. E. Marion, C. Bil. The prediction of ship motions and attitudes using artificial neural networks.19th National Conference of the Australian Society for Operations Research, Melbourne, Victoria,2007.
[25]Michael I. Jordan, David E. Rumelhart. Forward model:Supervised learning with a distal teacher. Cognitive Science,16,307-354,1992.
[26]金龙.神经网络气象预报建模理论方法与应用.2004.
[27]Javier Contreras, Rosario Espinola, Francisco J. Nogales, et al. ARIMA Models to predict next-day electricity prices. IEEE Transactions on power systems, Vol.18, No.3, August 2003.
[28]Grenier Y. Time-dependent ARMA modeling of non-stationary signals IEEE Trans Acoust Speech, Signal Processing,1983,3:899-911.
[29]M. Hall, A. V. Oppenheim, A. Willsky. Time-varying parametric modeling of speech. Proc IEEE Decision Contr. Conf, New York:IEEE Inc,1977.1085-1091.
[30]George Galanis, George Emmanouil, Peter C. Chu, George Kallos "A new methodology for the extension of the impact of data assimilation on ocean wave prediction". Ocean Dynamics (2009) 59:523-535.
[31]N. E. Huang, Z. Shen, Steven R. Long, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc. R. Soc. Lond. A (1998) 454,903-995.
[32]Donghoh Kim, Seung-Hyum Paek, Hee-Seok Oh. A Hilbert-Huang transform approach for predicting cyber-attacks. Journal of the Korean Statistical Society 37(2008) 277-283.
[33]伍春香,刘琳,王葆元.三层BP网隐层节点数确定方法的研究.武汉测绘科技大学学报,24(2),1999.
[34]张善文,雷英杰,冯有前MATLAB在时间序列分析中的应用[M].西安电子科技大学出版社,2007.
[35]张德丰等,MATLAB神经网络应用设计.机械工业出版社,2009.
[36]阮沈勇,王永利,桑群芳.MATLAB程序设计,电子工业出版社,2004.
[37]施晓红,周佳.精通GUI图形界面编程.北京大学出版社,2003.
[38]孟令金.基于EMD和AR的船舶运动极短期预报问题研究,哈尔滨工程大学硕士学位论文,2008.
[39]蒋庆华,一种基于小波变换及自回归模型的网络流量预测算法.吉林大学硕士学位论文,2006.
[40]陈烈,张永明,齐维贵等.基于RBF神经网络的时间序列交叉供热符合预报研究.电子学报,37(11)2009.
[41]张铃,张钹.人工神经网络理论及应用.杭州：浙江科学技术出版社.1997.
[42]伍尤桂,李元,王炜忻等.应用时间序列分析,广西师范大学出版社,1999.
[43]李建华.基于BP神经网络的二手船船价指数预测研究.大连海事大学硕士学位论文,2008.
[44]魏艳强.基于RBF神经网络的货运量预测模型研究.天津理工大学硕士学位论文,2007.
[45]韩忠玲.分形高斯噪声Hurst参数估计的实验评价.华东师范大学硕士学位论文,2008.
[2]安鸿志,陈兆国,杜金观,潘一民.时间序列的分析与应用[M].北京：科学出版社,1983
[3]杨叔子,吴雅,轩建平等.时间序列分析的工程应用[M].武汉：华中科技大学出版社,2007.
[4]袁振洲.应用自回归积分移动平均法预测铁路货源货流发展趋势.铁道学报.1996年4月
[5]David E. Rumelhart, James L. McClelland. Parallel Distributed Processing: Exploration in the Microstructure of Cognition. Cambridge:MIT Press,1986.
[6]Lapedes. A, Faber. R. Non-linear Signal Processing Using Neural Networks: Prediction and System Modeling. Los Alamos National Laboratory Report,1987
[7]J. Moody, C. Darken. Fast learning in networks of locally-tuned processing units. Neural Computation,1989, (1):281-294.
[8]Leonard Studer, Francesco Masulli. Building a neuro-fuzzy system to efficiently forecast chaotic time series[J]. Nuclear Instruments and Methods in Physics Research A 389(1997) 264-267.
[9]Roman Rosipal, Milos Koska, Igor Farkas. Prediction of chaotic time-series with a resource-allocating RBF network[J]. Neural Processing Letters 7:185-197,1998.
[10]杨红卫,何晨.基于人工神经网络的毫米波雨衰减预测.上海交通大学学报.2001,35(1)：13-16.
[11]吴微,陈维强.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.
[12]周德懋,李舟军,康荣雷.基于时间序列分析的网络流量预测模型研究.现代电子技术,2009年第8期.
[13]周惠,时间序列预测方法在港口行业中的应用.中国农业大学硕士学位论文.2004.
[14]杨建萍.基于ARIMA模型的用电量时间序列建模和预报.工程数学学报,25(4),2008.
[15]张利,基于时间序列ARIMA模型的分析预测算法研究及系统实现.江苏 大学硕士学位论文,2008.
[16]S.M.潘迪斯,吴宪民.时间序列及系统分析与应用[M].北京：机械工业出版社,1988
[17]张树京,齐立心.时间序列分析简明教程.清华大学出版社,北方交通大学出版社,2003.
[18]王燕.应用时间序列分析.中国人民大学出版社,2005.
[19]朱文谱,郜焕秋,谢楠等.船舶运动自适应TAR模型预报方法.中国船舶科学研究中心技术报告,1997.
[20]Holger R. Maier, Graeme C. Dandy. Neural networks for the prediction and forecasting of water resources variables:a review of modeling issues and applications. Environmental Modelling & Software 15(2000) 101-124.1999.
[21]I. A. Basheer, M. Hajmeer. Artificial neural networks:fundamentals, computing, design, and application. Journal of Microbiological Methods 43(2000) 3-31,2000.
[22]Donald F. Specht. A General Regression Neural Network. IEEE Transaction on Neural Networks Vol.2. No.6. November,1991.
[23]D. C. Park, M. A. El-Sharkawi, R. J. Marks Ⅱ, et al. Electric load forecasting using an artificial neural network. IEEE Transaction on Power Systems, Vol.6, No.2, May 1991.
[24]A. A. Khan, K. E. Marion, C. Bil. The prediction of ship motions and attitudes using artificial neural networks.19th National Conference of the Australian Society for Operations Research, Melbourne, Victoria,2007.
[25]Michael I. Jordan, David E. Rumelhart. Forward model:Supervised learning with a distal teacher. Cognitive Science,16,307-354,1992.
[26]金龙.神经网络气象预报建模理论方法与应用.2004.
[27]Javier Contreras, Rosario Espinola, Francisco J. Nogales, et al. ARIMA Models to predict next-day electricity prices. IEEE Transactions on power systems, Vol.18, No.3, August 2003.
[28]Grenier Y. Time-dependent ARMA modeling of non-stationary signals IEEE Trans Acoust Speech, Signal Processing,1983,3:899-911.
[29]M. Hall, A. V. Oppenheim, A. Willsky. Time-varying parametric modeling of speech. Proc IEEE Decision Contr. Conf, New York:IEEE Inc,1977.1085-1091.
[30]George Galanis, George Emmanouil, Peter C. Chu, George Kallos "A new methodology for the extension of the impact of data assimilation on ocean wave prediction". Ocean Dynamics (2009) 59:523-535.
[31]N. E. Huang, Z. Shen, Steven R. Long, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc. R. Soc. Lond. A (1998) 454,903-995.
[32]Donghoh Kim, Seung-Hyum Paek, Hee-Seok Oh. A Hilbert-Huang transform approach for predicting cyber-attacks. Journal of the Korean Statistical Society 37(2008) 277-283.
[33]伍春香,刘琳,王葆元.三层BP网隐层节点数确定方法的研究.武汉测绘科技大学学报,24(2),1999.
[34]张善文,雷英杰,冯有前MATLAB在时间序列分析中的应用[M].西安电子科技大学出版社,2007.
[35]张德丰等,MATLAB神经网络应用设计.机械工业出版社,2009.
[36]阮沈勇,王永利,桑群芳.MATLAB程序设计,电子工业出版社,2004.
[37]施晓红,周佳.精通GUI图形界面编程.北京大学出版社,2003.
[38]孟令金.基于EMD和AR的船舶运动极短期预报问题研究,哈尔滨工程大学硕士学位论文,2008.
[39]蒋庆华,一种基于小波变换及自回归模型的网络流量预测算法.吉林大学硕士学位论文,2006.
[40]陈烈,张永明,齐维贵等.基于RBF神经网络的时间序列交叉供热符合预报研究.电子学报,37(11)2009.
[41]张铃,张钹.人工神经网络理论及应用.杭州：浙江科学技术出版社.1997.
[42]伍尤桂,李元,王炜忻等.应用时间序列分析,广西师范大学出版社,1999.
[43]李建华.基于BP神经网络的二手船船价指数预测研究.大连海事大学硕士学位论文,2008.
[44]魏艳强.基于RBF神经网络的货运量预测模型研究.天津理工大学硕士学位论文,2007.
[45]韩忠玲.分形高斯噪声Hurst参数估计的实验评价.华东师范大学硕士学位论文,2008.