基于信息熵及粒子群优化算法的模糊时间序列预测模型研究
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摘要
随着金融全球化进程的不断加快,中国金融也更深更广的融入到世界经济中。为能更好更快地适应金融全球化带来的全新经济环境,精确的金融市场预测扮演着不可或缺的角色。金融时间序列作为金融市场中最重要的数据类型之一,对其进行准确合理的预测能够有效地指导金融投资者的投资行为和政府调控行为。鉴于时间序列分析应用的广泛性,目前已有众多学者对其进行了各方面的研究。但由于金融时间序列本身具有的高频性、多维度、非线性、模糊性等特征,极大地增加了对金融时间序列进行分析的难度。
近年来模糊时间序列在时间序列分析上的应用备受瞩目,针对如何提高模糊时间序列预测模型的精度,目前主要集中在如何客观有效划分论域区间及如何建立有效的模糊逻辑关系矩阵这两方面进行改进与创新。本文在前人工作基础上,提出两种新算法对模糊时间序列中存在的这两个问题进行改进。具体内容总结如下:
(1)为能有效构建模糊逻辑关系,本文将信息熵概念引入到模糊集中,使得模糊集能较合理地对数据集进行模糊化处理。通过对阿拉巴马大学入学人数、上证综指、道琼斯工业指数、美元对日元汇率等数据集的预测结果表明,信息、熵的引入使模糊集具有更好的适应性及鲁棒性,同时也大大降低了计算隶属度的复杂性,使得算法具有较好的可执行性。
(2)为能客观有效地对论域区间进行划分,本文利用粒子群优化算法的随机搜索性能得出全局最优位置,即论域区间中点。通过与众多已存在的金融时间序列预测模型对比,该算法的引入能很好地解决模糊时间序列中存在人为划分论域的不足,同时也极大地提高了模型的预测精度。
With the globalization of finance developing rapidly, the Chinese finance is also deeper and broader integrating to the world economics. To adapt the new economic environment better and quickly, the standards of accuracy in forecasting have reached higher and higher. The accurate and reasonable forecasting of the finance time series as the important data type of finance market was able to instruct the financial investors' investment and the government regulation effectively. In view of the fact that the application of the finance time series analysis is very widespread, the numerous scholars have researched to it in various aspects. However, the finance time series have some characteristics such as high frequency, multi-dimensions, misalignment and fuzziness. which increased the difficulty of study the finance time series.
Recentlt, the fuzzy time series have attracted much attention in the application of finance time series analysis. All researchers in the domain of fuzzy time series have paid much attention to the existing unsolved problems, i.e., how to partition the universe of discourse and how to construct the fuzzy logic relationships effectively. This article proposed two new algorithms to solve these questions which existed in fuzzy time series based on the predecessor works. The actual content summary is as follows:
(1) To construct the fuzzy logic relations effectively, this article introduces the information entropy concept to the fuzzy set to enables the fuzzy set defuzzy the date set reasonably. Through the forecasting results of Alabama university enrollment number,000001, the Dow Jones average, USD/JPY exchange rate and so on, which indicated that introduction of the information entropy have enabled the fuzzy set have better compatibility and robustness, at the same time reduced the complexity degree of computation and made the algorithm have better performability.
(2) To divisie the universe of discourse effectively and objectively, this article uses the particle swarm optimization with the random searching performance to optimize position obtains, namely universe of discourse middle point. Compared to numerous forecasting models, the proposed models not only solve the problem of artificial division universe of discourse, but also provide better forecasting performance and obtain higher accuracy rates than the existing models.
近年来模糊时间序列在时间序列分析上的应用备受瞩目,针对如何提高模糊时间序列预测模型的精度,目前主要集中在如何客观有效划分论域区间及如何建立有效的模糊逻辑关系矩阵这两方面进行改进与创新。本文在前人工作基础上,提出两种新算法对模糊时间序列中存在的这两个问题进行改进。具体内容总结如下:
(1)为能有效构建模糊逻辑关系,本文将信息熵概念引入到模糊集中,使得模糊集能较合理地对数据集进行模糊化处理。通过对阿拉巴马大学入学人数、上证综指、道琼斯工业指数、美元对日元汇率等数据集的预测结果表明,信息、熵的引入使模糊集具有更好的适应性及鲁棒性,同时也大大降低了计算隶属度的复杂性,使得算法具有较好的可执行性。
(2)为能客观有效地对论域区间进行划分,本文利用粒子群优化算法的随机搜索性能得出全局最优位置,即论域区间中点。通过与众多已存在的金融时间序列预测模型对比,该算法的引入能很好地解决模糊时间序列中存在人为划分论域的不足,同时也极大地提高了模型的预测精度。
With the globalization of finance developing rapidly, the Chinese finance is also deeper and broader integrating to the world economics. To adapt the new economic environment better and quickly, the standards of accuracy in forecasting have reached higher and higher. The accurate and reasonable forecasting of the finance time series as the important data type of finance market was able to instruct the financial investors' investment and the government regulation effectively. In view of the fact that the application of the finance time series analysis is very widespread, the numerous scholars have researched to it in various aspects. However, the finance time series have some characteristics such as high frequency, multi-dimensions, misalignment and fuzziness. which increased the difficulty of study the finance time series.
Recentlt, the fuzzy time series have attracted much attention in the application of finance time series analysis. All researchers in the domain of fuzzy time series have paid much attention to the existing unsolved problems, i.e., how to partition the universe of discourse and how to construct the fuzzy logic relationships effectively. This article proposed two new algorithms to solve these questions which existed in fuzzy time series based on the predecessor works. The actual content summary is as follows:
(1) To construct the fuzzy logic relations effectively, this article introduces the information entropy concept to the fuzzy set to enables the fuzzy set defuzzy the date set reasonably. Through the forecasting results of Alabama university enrollment number,000001, the Dow Jones average, USD/JPY exchange rate and so on, which indicated that introduction of the information entropy have enabled the fuzzy set have better compatibility and robustness, at the same time reduced the complexity degree of computation and made the algorithm have better performability.
(2) To divisie the universe of discourse effectively and objectively, this article uses the particle swarm optimization with the random searching performance to optimize position obtains, namely universe of discourse middle point. Compared to numerous forecasting models, the proposed models not only solve the problem of artificial division universe of discourse, but also provide better forecasting performance and obtain higher accuracy rates than the existing models.
引文
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[2]王振龙,胡永宏：应用时间序列分析[M].北京：科学出版社,2007.
[3]张拥华.基于支持向量机的金融时间序列研究.硕士学位论文,湖南大学.2008.5.
[4]吴怀宇：时间序列分析与综合[M].武汉,武汉大学出版社,,2005.
[5]兰秋军：金融时间序列隐含模式挖掘方法及其应用研究.博士学位论文,湖南大学,2004.10.
[6]特伦斯.C.米尔斯著,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.(第二版)
[7]G.P. Box, G.M. Jenkins:Time series Analysis:Forecasting and Control[M].Holden-Day, San Francisco. CA.1976.
[8]R.F.Engle. Autoregressive conditional heteroskedasticity with estimates of the variance of UK inflation, Econometrica.1982,50:987-1008.
[9]T.Bollerslev, Generalized autoregressive conditional heteroscedasticity, J. Econometrics,1986, 31:307-327.
[10]Gorr W:Research prospective on neural network forecasting. International Journal of Forecasting 1994; 10:1-4.
[11]Choi. J.H., Lee. M.K.,& Lee. M.W. Trading S & P 500 stock index futures using a neural network[C]. Proceedings of the third annual international conference on artificial intelligence applications on wall street (pp.63-72). New York.1995.
[12]Q. Song. B.S. Chissom, "Fuzzy time series and its models," Fuzzy Sets and Systems. Vol.54, pp.269-277,1993.
[13]Q. Song, B.S. Chissom,"Forecasting enrollments with fuzzy time series-part 1," Fuzzy Sets and Systems, vol.54, pp.1-9,1993.
[14]Q. Song, B.S. Chissom, "Forecasting enrollments with fuzzy time series-part 2," Fuzzy Sets and Systems, vol.62, pp.1-8,1994.
[15]Zadeh, L. A.,"The concept of a linguistic variable and its application to approximate reasoning I," Information Science, vol.8. pp.199-249,1975.
[16]Zadeh, L. A., "The concept of a linguistic variable and its application to approximate reasoning Ⅱ," Information Science, vol.8, no.8, pp.301-357,1975.
[17]Zadeh, L. A., "The concept of a linguistic variable and its application to approximate reasoning III." Information Science, vol.9. pp.43-80,1975.
[18]Zadeh, L. A., "Fuzzy sets. Inform and Control." vol.8. pp.338-353.1965.
[19]Chen SM:Forecasting enrollments based on fuzzy time series. Fuzzy Sets and Systems 1996:81(3):311-319.
[20]Hwang, J.R., Chen, S.M., and Lee. C.H.:Handling forecasting problems using fuzzy time series. Fuzzy Sets and Systems.100:217-228.1998.
[21]Huarng K:Effective lengths of intervals to improve forecasting in fuzzy time series. Fuzzy Sets and Systems 2001;123(3):387-394.
[22]Huarng K:Heuristic models of fuzzy time series for forecasting. Fuzzy Sets and Systems 2001:123(3):369-386.
[23]Chen SM:Forecasting enrollments based on high-order fuzzy time series. Cybernetics and Systems 2002:33(1):1-16.
[24]Chen SM, Hwang JR:Temperature prediction using fuzzy time series. IEEE Transactions on Systems. Man. and Cybernetics-Part B:Cybernetics 2000:30(2):263-275.
[25]L.W. Lee, S.M. Chen, and Y.H. Leu:A new method for handling forecasting problems based on two-factor high-order Fuzzy Time Series. Proceedings of the 2004 ninth conference on artificial intelligence and applications, Taipei. Taiwan, Republic of China, November 2004.
[26]Kunhuang Huarng. Tiffany Hui-Kuang Yu:The application of neural networks to forecast fuzzy time series. Physica A 363(2006)481-491.
[27]H.K. Yu, Weighted fuzzy time-series models for TAIEX forecasting. Physica A 349(2004)609-624.
[28]Tai-Liang Chen, Ching-Hsue Cheng, Hia Jong Teoh:Fuzzy time-series based on Fibonacci sequence for stock price forecasting. Physica A 2007;380:377-390.
[29]Tai-Liang Chen, Ching-Hsue Cheng, Hia Jong Teoh:High-order fuzzy time-series based on multi-period adaptation model for forecasting stock markets. Physica A 387(2008)876-888.
[30]Chen, S.M., Chung, N.Y.:Forecasting enrollments of students by using fuzzy time series and genetic algorithms. International Journal of Information and Management Sciences,17(3):1-17, 2006.
[31]Chen, S.M., Chung, N.Y.:Forecasting enrollments using high-order fuzzy time series and genetic algorithms. International Journal of Intelligent Systems,21(5):485-501,2006.
[32]Ching-Hsue Cheng, Guang-Wei Cheng, Jia-Wen Wang:Multi-attribute fuzzy time series method based on fuzzy clustering. Expert Systems with Applications 2008;34(2):1235-1242.
[33]Li-Wei Lee, Li-Hui Wang. Shyi-Ming Chen:Temperature prediction and TAIFEX forecasting based on high-order fuzzy logical relationships and genetic simulated annealing techniques. Expert Systems with Applications 2008;34(1):328-336.
[34]Chia-Ching Hsu. Shyi-Ming Chen:A new method for forecasting enrollments based on fuzzy time series. Proceedings of the Seventh Conference on Artificial Intelligence and Applications, Taichung. Taiwan, Republic of China.17-22,2002.
[35]C.H.Cheng. R.J.Chang. C.A.Yeh:Entropy-based and trapezoid fuzzification-based fuzzy time series approach for forecasting IT project cost. Technological Forecasting and Social Change 2006;73(5):524-542.
[36]迟凯.车文刚.付芳萍：基于FCM的模糊时间序列模型及人民币汇率预测(第29届中国控制会议)
[37]Kai Chi. Fangping Fu.Wengang Che. A novel model of fuzzy time series based on K-means clustering. Proceeding of 2nd International Workshop on Education Technology and Computer Science,2010. Vol.1. pp.223-225. (El. ISTP.)
[38]Emad Elbeltagi. Tarek Hegazy, Donald Grierson:Comparison among five evolutionary-based optimization algorithm. Advanced Engineering Informatics,19(1):43-53.2005.
[39]I-Hong Kuo. Shi-Jinn Horng. Tzong-Wann Kao. et al:Yi Pan:An improved method for forecasting enrollments based on fuzzy time series and particle swarm optimization. Expert Systems with Applications:36(3):6108-6117.2009.
[40]I-Hong Kuo. Shi-Jinn Horng, Yuan-Hsin Chen, et al:Forecasting TAIFEX based on fuzzy time series and particle swarm optimization. Expert Systems with Applications; 37(2):1494-1502.2010.
[41]Jin-Ⅱ Park, Dae-Jong Lee, Chang-Kyu Song, et al:TAIFEX and KOSPI 200 forecasting based on two-factors high-order fuzzy time series and particle swarm optimization. Expert Systems with Applications; 37(2):959-967,2010.
[42]Kai Chi, Fangping Fu, Wengang Che, Second order difference heuristic model of fuzzy time series based on particle swarm optimization, The 2nd International Conference on Computer Engineering and Technology,2010, In Press. (El. ISTP)
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