时间序列模型的误差分析与研究
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摘要
随着经济的发展和人们生活水平的提高及投资意识的转变,人们对证券股票投资的热情越来越高,股票投资已成为经济投资的一个重要组成部分,成为一个国家的经济生活和社会生活中所不可缺少的一部分。面对瞬息万变的股票市场,投资者在进行投资活动时将面临许多不确定性因素。为了追求投资收益的最大化和投资风险的最小化,不断地探索股票时间序列的内在规律,寻找其有效的分析方法和工具就显得尤为重要了。因此,对金融时间序列模型误差的分析具有重要的理论意义和应用价值。
在时间序列分析中,一般采用建模的方法对数据进行拟合。在传统时间序列分析方法中,尽管可以得到趋势明朗后模型与实际数据的较好拟合效果,但是还是有一些时序点的拟合误差较大。本文利用时间序列分析方法对两支股票进行建模,围绕股票时间序列分析模型的拟合误差及异常误差值进行了深入的分析研究,得出结论：一方面,两个时间序列模型的异常误差值出现所对应的时间序列点基本一致；另一方面,两个时间序列模型的误差波动情况具有一定的同步性。这说明在运用时间序列模型分析股价时间序列时,模型的误差大小、误差变化以及异常误差的产生与分析对象的大小无关。
本文采用金钼股份(601958)和出版传媒(601999)的120个交易日收盘价数据,分析时间序列模型的误差值和异常误差,并对异常时序点的价格变化率进行分析,分析结果表明,股票时间序列模型误差的影响主要来自于外界因素对分析对象属性变化程度的影响。模型拟合效果与被拟合对象之间的关键点不在于对象本身的属性特征,而是在于外界因素对被拟合对象属性的刺激影响上。来自股票外界的因素影响了股票属性的变化方向和变化程度,表现为价格的上涨与下跌和涨幅与跌幅的大小。这一结论在今后时间序列模型的理论分析和实际应用中具有指导性和实用性。此外本文研究了适用于时间序列模型误差的异常误差值检测方法,较传统的离群值分析检测方法有所改进。
With the development of economy and the conversion of people's investment consciousness, the people's investing enthusiasm of stock is higher and higher.Stock investment becomes an important part of economy investment, and also an important part of people's life in modern times. In the face of the fast changing stock market, investors will face a lot of uncertain factors while carrying on investing in stock market. Through researches into its internal disciplinarian, effective analytic methods and tools are being looked for more interest with lower risk. Therefore the study of disciplinarian in the model error of financial time series has great theoretical significant and applicable value.
Modeling methods are generally used in fitting security time series. In the traditional time series analyzing methods, the fitting results are effective in clear tendency, but some fitting errors are relatively great. This paper uses the time series analyzing methods to build the model for two different stocks, deeply analyze and research on the stock fitting error and unusual error. The analysis conclusions as follows:on one hand, the unusual errors of two different time series model almost have the same time point; on another hand, the errors fluctuate with almost a same step. It shows when we analyze the stock price series with the time series model, the model error size, the model error changing situation, and the production of unusual error are irrelevant with the size of analytic target.
In this paper, the analyze data come from the close-price in one hundred and twenty trading days of Jinmu stock (601958) and Chubanchuanmei stock (601999).After analyze the model error, model unusual error and the price changing rate, the result shows that the influence to stock's time series model error mainly produced by the influence of external factors act on the intensity of the attribute of analytic target.The key point of model fitting result doesn't lie in the target's own attributive character, but in the influence that external factors act on. The external factors influence the attributive character's changing direction and intensity, it is shown as the direction of price rising or reducing, and amount of price rising or reducing. This conclusion will be guidance and practicality in theory analyzing for time series model in future. In this paper, a suitable method for detecting the unusual error in time series model is researched, and it's an improved method than the traditional analysis of the outlier detection.
在时间序列分析中,一般采用建模的方法对数据进行拟合。在传统时间序列分析方法中,尽管可以得到趋势明朗后模型与实际数据的较好拟合效果,但是还是有一些时序点的拟合误差较大。本文利用时间序列分析方法对两支股票进行建模,围绕股票时间序列分析模型的拟合误差及异常误差值进行了深入的分析研究,得出结论：一方面,两个时间序列模型的异常误差值出现所对应的时间序列点基本一致；另一方面,两个时间序列模型的误差波动情况具有一定的同步性。这说明在运用时间序列模型分析股价时间序列时,模型的误差大小、误差变化以及异常误差的产生与分析对象的大小无关。
本文采用金钼股份(601958)和出版传媒(601999)的120个交易日收盘价数据,分析时间序列模型的误差值和异常误差,并对异常时序点的价格变化率进行分析,分析结果表明,股票时间序列模型误差的影响主要来自于外界因素对分析对象属性变化程度的影响。模型拟合效果与被拟合对象之间的关键点不在于对象本身的属性特征,而是在于外界因素对被拟合对象属性的刺激影响上。来自股票外界的因素影响了股票属性的变化方向和变化程度,表现为价格的上涨与下跌和涨幅与跌幅的大小。这一结论在今后时间序列模型的理论分析和实际应用中具有指导性和实用性。此外本文研究了适用于时间序列模型误差的异常误差值检测方法,较传统的离群值分析检测方法有所改进。
With the development of economy and the conversion of people's investment consciousness, the people's investing enthusiasm of stock is higher and higher.Stock investment becomes an important part of economy investment, and also an important part of people's life in modern times. In the face of the fast changing stock market, investors will face a lot of uncertain factors while carrying on investing in stock market. Through researches into its internal disciplinarian, effective analytic methods and tools are being looked for more interest with lower risk. Therefore the study of disciplinarian in the model error of financial time series has great theoretical significant and applicable value.
Modeling methods are generally used in fitting security time series. In the traditional time series analyzing methods, the fitting results are effective in clear tendency, but some fitting errors are relatively great. This paper uses the time series analyzing methods to build the model for two different stocks, deeply analyze and research on the stock fitting error and unusual error. The analysis conclusions as follows:on one hand, the unusual errors of two different time series model almost have the same time point; on another hand, the errors fluctuate with almost a same step. It shows when we analyze the stock price series with the time series model, the model error size, the model error changing situation, and the production of unusual error are irrelevant with the size of analytic target.
In this paper, the analyze data come from the close-price in one hundred and twenty trading days of Jinmu stock (601958) and Chubanchuanmei stock (601999).After analyze the model error, model unusual error and the price changing rate, the result shows that the influence to stock's time series model error mainly produced by the influence of external factors act on the intensity of the attribute of analytic target.The key point of model fitting result doesn't lie in the target's own attributive character, but in the influence that external factors act on. The external factors influence the attributive character's changing direction and intensity, it is shown as the direction of price rising or reducing, and amount of price rising or reducing. This conclusion will be guidance and practicality in theory analyzing for time series model in future. In this paper, a suitable method for detecting the unusual error in time series model is researched, and it's an improved method than the traditional analysis of the outlier detection.
引文
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[2]R.N. Mantegna, H.E. Stanley. An Introduction to Econophysics:Correlations and Complexity in Finance. Cambridge University Press,2000.
[3]Fama, E.F., MacBeth, J.D.'Risk, Return, and Equilibrium:Empirical Tests'. Journal of Political Economy,1973,81:607-36.
[4]Cox, J.C., Rubinstein, M. Options Markets. In:Pretice-Hall:Englewood Cliffs, New Jersey,1985.
[5]Hull, J.C. Options, Futures, and Other Derivatives. In:3rd ed. Prentice-Hall:Upper Saddle River, New Jersey,1997.
[6]周洪涛,王宗军.基于混沌理论的上海股市非线性动力学研究[J].系统工程理论方法应用,2005,14(5)：390-394.
[7]马千里,郑启伦,彭宏,钟谭卫.基于相空间重构理论与递归神经网络相结合的股票短期预测方法[J].计算机应用研究,2007,24(4)：239-241.
[8]G. Peter Zhang. Time series forecasting using a hybrid ARIMA and neural network model [J]. Neurocomputing,2003(50):159-175.
[9]Terence C. Mills著,俞卓菁译.金融时间序列的经济计量学模型[M].北京：经济科学出版社,2002.
[10]Ruey S. Tsay著,潘家柱译.金融时间序列分析[M].北京：机械工业出版社,2007.
[11]C.W.J. Granger, A.P. Anderson. An Introduction to Bilinear Time Series Models, Vandenhoeck & Ruprecht,1978.
[12]H. Tong, K.S. Lim, Threshold autoregressive, limit cycles and cyclical data, J. R.Stat. Soc, Ser. B,1980,42 (3):245-292.
[13]R.F.Engle, Autoregressive conditional heteroskedasticity with estimates of the variance of UK inflation, Econometrica,1982,50:987-1008.
[14]T.Bollerslev, Generalized autoregressive conditional heteroscedasticity, J. Econometrics,1986,31:307-327.
[15]D.A. Hsieh, Chaos and nonlinear dynamics:application to financial markets, J. Finance, 1991,46:1839-1877.
[16]Mehdi Khashei, Mehdi Bijari, Gholam Ali Raissi Ardali. Improvement of Auto-Regressive Integrated Moving Average models using Fuzzy logic and Artificial Neural Networks (ANNs) [J]. Neurocomputing,2008.
[17]Kyoung-jae Kim. Artificial neural networks with evolutionary instance selection for financial forecasting [J]. Expert Systems with Applications,2006 (30):519-526.
[18]B.Whitehead, W.A.Hoyt. Function approximation approach to anomaly detection in propulsion system test data [J]. Journal of Propulsion and Power,1995, 11(5): P1074-1076.
[19]Dipanker Dasgupta, Stephanie Forrest. Novelty detection in time series data using ideas from immunology[C]. Proceedings of the 5th International Conference on Intelligent System.1996:P82-87.
[20]C. Shahabi, X. Tian, w. Zhao. Tsa-Tree:A wavelet-based approach to improve the efficiency of multi-level surprise and trend queries [C]. Proceedings of 12th International Conference on Scientific and Statistical Database Management. Washington:IEEE Computer Society,2000:P55-68.
[21]E. Keogh, S Lonardi, W Chiu. Finding surprising patterns in a time series database in linear time and space[C]. Proceedings of the 8th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York:ACM Press.2002: P550-556.
[22]Kenji Yamanishi, Junichi Takeuchi. A unifying framework for detecting outliers and change points from non-stationary time series data[C]. Proceedings of 8th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York:ACM Press,2002:P676-681.
[23]肖辉.时间序列的相似性查询与异常检测[D].上海：复旦大学计算机软件与理论专业,2005.
[24]肖立中,邵志清.基于序列分析的报警综合处理研究[J].计算机工程与应用,2006，42(8)：P152-154.
[25]钱昱,郑诚.基于序列模式的异常检测[J].微机发展,2004，14(9)：P53-55.
[26]杨虎,王会琦,程代杰.基于预测的序列异常数据挖掘[J].计算机科学,2004,31(4)：P117-119.
[27]肖辉,胡运发.基于分段时问弯曲距离的时间序列挖掘[J].计算机研究与发展,2005,42(1)：P72-78.
[28]林孔元,刘正光，郭爱民,方惠如.重油催化裂化稳态过程数据协调与检测[J].天津大学学报，1996：29(4),P631-636．
[29]Lu G, Lachapelle G. Statistical Quality for Kinematic GPS Position [J]. Manuscripta Geodaetica,1992,17:270-283.
[30]王国富,朱建军.含有粗差观测值的白适应滤波[J].测绘通报,2004(4)：P19-21.
[31]陶本藻.卡尔曼滤波模型误差的识别[J].地壳形变与地震,1999，19(4)：P15-20.
[32]周柏贤.网络流量异常检测与预测方法研究[D].北京：中国科学院计算技术研究所,2003
[33]詹艳艳,陈晓云,徐荣聪.基于时间序列模式表示的异常检测算法[J].计算机应用研究,2007,24(11)：P96-99.
[34]汪斐.在线的时间序列异常检测算法研究[D].广州：中山大学计算机软件与理论专业,2008.
[35]李鹤松.证券时间序列中的信息奇异点研究与建模[D].云南：昆明理工大学模式分析与模式识别专业,2009.
[36]陈华,李继波.异常(Outlier)检测算法综述[J].大众科技,2005,9：P96-97.
[37]黄洪宇,林甲祥,陈崇成,樊明辉.离群数据挖掘综述[J].计算机应用研究,2006,8：P8-13.
[38]张彦霞,赵永恒.离群数据的探测[J].天文学进展,2004，22(1).
[39]李招财,戴燕萍.统计中离群值(可疑值)的判定办法[J].井冈山医专学报,2000,7(2).P58.
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