中国股票市场非线性的实证与应用研究
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摘要
本论文来自教育部博士点基金项目“中国股票市场混沌与分形研究”。
有效市场假说是现代一系列经典金融理论的基础，经多年之发展，已被广泛应用于资本市场的研究。然而随着一些异常想象的出现和非线性理论的发展，人们开始逐渐认识到线性范式的缺陷和失灵，非线性的理论和方法正在成为金融舞台上的主角。本文依照严谨的逻辑关系从资本市场线性理论的基石——有效市场假说入手，从其传统的检验方法展开，指出了传统方法的局限性，必将使用非线性的分析方法来研究资本市场。然而实证的结果却发现现实的情况却和有效市场假说相悖，中国股票市场是一个非线性的动力系统，并且具有显著的混沌、分形的特征。这一发现将帮助我们从新的角度来认识中国的股票市场，并指导我们更好的把握市场规律。
全文共分四章。
第一章——股票市场中的线性理论及失灵。介绍了资本市场理论的基石——有效市场假说及其发展，以及以其为基础发展起来的其他经典的线性模型；使用传统的检验方法如游程检验、误差项序列相关检验和ADF单位根检验对有效市场假说的弱形式进行了实证检验，并提出传统检验方法的局限性；分析了股票市场中与EMH相悖的反常想象，提出线性范式的失灵，需要用非线性的理论和方法研究资本市场。
第二章——股票市场的非线性理论的研究现状。概括地介绍了非线性理论中最重要的两大领域：混沌和分形的基本理论、特征描述，并概括地总结了国内外关于混沌、分析理论的研究成果。
第三章——中国股票市场非线性理论的实证研究。用正态性检验、GARCH检验、长期记忆分析等对我国股票市场进行了非线性的存在性研究，计算了混沌的特征量Lyapunov指数和分形维数。实证分析的结果表明市场有效假说的线性假定是不符合实际的，中国股票市场是一个非线性的动力系统，具有显著的混沌、分形的特征。
第四章——非线性理论在股票市场中的应用研究。重点关注分形理论在股票
市场中的应用—分形市场假说、非线性理论在投资组合理论中的应用这两大方
面;深入探讨了Levy分布对我国股票市场收益率分布的描述问题。
论文做了如下创新性研究工作:①采用复杂科学的系统思维来研究资本市
场，采用定性定量相结合的理论框架。②运用GARCH、RBF、侧S等检验方法
和智能算法，并大量使用计算机模拟的实证分析，以认识资本市场的复杂性。③
提出了非正态稳定分布条件下的风险度量工具和投资组合模型。④深入探讨了
Levy分布对我国股票市场收益率分布的描述问题。
This thesis comes from the project: 'A Research on the Chaos and Fractal in China Stock Market', which is funded by ministry of education.
Efficient Market Hypothesis is the foundation of a series of modern classic theories in finance, and it has been applied widely on the research in the capital market. However, with the development of non-linear theories and the appearance of many abnormities in the market, people have begun to realize the limitation and the failure of linear theories, and non-linear theories and methods have become the leading actor. This paper begins with the EMH and its traditional test methods. According to strict logicality, we find out the limitation of old test methods and only non-linear analytical method can study the capital market. Furthermore the results of the empirical study reveal that the realistic situation is contrary to EMH and China's stock market is a non-linear dynamical system and possesses remarkable Chaos and Fractal characteristics. This discovery will help us to understand the stock market of China with new point of view, and guide us to grasp the rules of the market better.
This paper includes four chapters.
The first chapter-the linear theories in stock market and the invalidation. On
the one hand, the author introduces the foundation of the capital market theory -Efficient market hypothesis and some other classical linear models that are based on it; on the other hand, the author uses the traditional methods such as the run test, the autocorrelation coefficients test and the ADF test to test the weak form of EMH with real data in China's stock market. Finally this chapter analyses some abnormal phenomena contrary to EMH in the stock market. From the results, the author puts forward that non-linear theories and methods should be used to study the capital market.
The second chapter-the current research of the non-linear theories in the
stock market. This chapter summarizes and introduces two major important fields in
non-linear theories: the Chaos and Fractal theory, and summarizes some current researches about them home and abroad.
The third chapter-the empirical research on the non-linear theories in China's
stock market. This chapter tests whether the non-linearity exists in China's stock market by normal distribution test, GARCH effect test, long-term memory test, etc. And it calculate the Lyapunov exponent and the fractal dimension, which indicate that EMH is not conform to reality market, and China's stock market is a non-linear dynamical system and possesses remarkable Chaos and Fractal features.
The fourth chapter-the application study of the non-linear theories in China's
stock market. This chapter pays close attention to two major applications in non-linear theories: Fractal market hypothesis and applications in portfolio models. At last, whether Levy distribution can be used for describe the distribution of stock returns in China is discussed.
The innovative work of the thesis: (1)adopt systematical and complex methods and a theoretical frame with qualitative and quantitative analyses to investigate complicated problems in capital market.(2)adopt some test methods and intelligent programs such as GARCH , RBF, and use various empirical analyses based on computer simulation to understand the complexity of the capital market.(3)propose the portfolio optimization model based on non-normal distribution, (4)discuss the problem whether Levy distribution can describe the distribution of returns of stock prices in China's stock market.
有效市场假说是现代一系列经典金融理论的基础，经多年之发展，已被广泛应用于资本市场的研究。然而随着一些异常想象的出现和非线性理论的发展，人们开始逐渐认识到线性范式的缺陷和失灵，非线性的理论和方法正在成为金融舞台上的主角。本文依照严谨的逻辑关系从资本市场线性理论的基石——有效市场假说入手，从其传统的检验方法展开，指出了传统方法的局限性，必将使用非线性的分析方法来研究资本市场。然而实证的结果却发现现实的情况却和有效市场假说相悖，中国股票市场是一个非线性的动力系统，并且具有显著的混沌、分形的特征。这一发现将帮助我们从新的角度来认识中国的股票市场，并指导我们更好的把握市场规律。
全文共分四章。
第一章——股票市场中的线性理论及失灵。介绍了资本市场理论的基石——有效市场假说及其发展，以及以其为基础发展起来的其他经典的线性模型；使用传统的检验方法如游程检验、误差项序列相关检验和ADF单位根检验对有效市场假说的弱形式进行了实证检验，并提出传统检验方法的局限性；分析了股票市场中与EMH相悖的反常想象，提出线性范式的失灵，需要用非线性的理论和方法研究资本市场。
第二章——股票市场的非线性理论的研究现状。概括地介绍了非线性理论中最重要的两大领域：混沌和分形的基本理论、特征描述，并概括地总结了国内外关于混沌、分析理论的研究成果。
第三章——中国股票市场非线性理论的实证研究。用正态性检验、GARCH检验、长期记忆分析等对我国股票市场进行了非线性的存在性研究，计算了混沌的特征量Lyapunov指数和分形维数。实证分析的结果表明市场有效假说的线性假定是不符合实际的，中国股票市场是一个非线性的动力系统，具有显著的混沌、分形的特征。
第四章——非线性理论在股票市场中的应用研究。重点关注分形理论在股票
市场中的应用—分形市场假说、非线性理论在投资组合理论中的应用这两大方
面;深入探讨了Levy分布对我国股票市场收益率分布的描述问题。
论文做了如下创新性研究工作:①采用复杂科学的系统思维来研究资本市
场，采用定性定量相结合的理论框架。②运用GARCH、RBF、侧S等检验方法
和智能算法，并大量使用计算机模拟的实证分析，以认识资本市场的复杂性。③
提出了非正态稳定分布条件下的风险度量工具和投资组合模型。④深入探讨了
Levy分布对我国股票市场收益率分布的描述问题。
This thesis comes from the project: 'A Research on the Chaos and Fractal in China Stock Market', which is funded by ministry of education.
Efficient Market Hypothesis is the foundation of a series of modern classic theories in finance, and it has been applied widely on the research in the capital market. However, with the development of non-linear theories and the appearance of many abnormities in the market, people have begun to realize the limitation and the failure of linear theories, and non-linear theories and methods have become the leading actor. This paper begins with the EMH and its traditional test methods. According to strict logicality, we find out the limitation of old test methods and only non-linear analytical method can study the capital market. Furthermore the results of the empirical study reveal that the realistic situation is contrary to EMH and China's stock market is a non-linear dynamical system and possesses remarkable Chaos and Fractal characteristics. This discovery will help us to understand the stock market of China with new point of view, and guide us to grasp the rules of the market better.
This paper includes four chapters.
The first chapter-the linear theories in stock market and the invalidation. On
the one hand, the author introduces the foundation of the capital market theory -Efficient market hypothesis and some other classical linear models that are based on it; on the other hand, the author uses the traditional methods such as the run test, the autocorrelation coefficients test and the ADF test to test the weak form of EMH with real data in China's stock market. Finally this chapter analyses some abnormal phenomena contrary to EMH in the stock market. From the results, the author puts forward that non-linear theories and methods should be used to study the capital market.
The second chapter-the current research of the non-linear theories in the
stock market. This chapter summarizes and introduces two major important fields in
non-linear theories: the Chaos and Fractal theory, and summarizes some current researches about them home and abroad.
The third chapter-the empirical research on the non-linear theories in China's
stock market. This chapter tests whether the non-linearity exists in China's stock market by normal distribution test, GARCH effect test, long-term memory test, etc. And it calculate the Lyapunov exponent and the fractal dimension, which indicate that EMH is not conform to reality market, and China's stock market is a non-linear dynamical system and possesses remarkable Chaos and Fractal features.
The fourth chapter-the application study of the non-linear theories in China's
stock market. This chapter pays close attention to two major applications in non-linear theories: Fractal market hypothesis and applications in portfolio models. At last, whether Levy distribution can be used for describe the distribution of stock returns in China is discussed.
The innovative work of the thesis: (1)adopt systematical and complex methods and a theoretical frame with qualitative and quantitative analyses to investigate complicated problems in capital market.(2)adopt some test methods and intelligent programs such as GARCH , RBF, and use various empirical analyses based on computer simulation to understand the complexity of the capital market.(3)propose the portfolio optimization model based on non-normal distribution, (4)discuss the problem whether Levy distribution can describe the distribution of returns of stock prices in China's stock market.
引文
1．徐绪松，复杂科学·资本市场·项目管理，科学出版社，2003年
2．徐绪松，陈彦斌，深沪股市分形维实证研究，数量经济与技术经济研究，2000年11期
3．徐绪松，陈彦斌，深沪股票市场非线性实证研究，数量经济技术经济研究，2001年3期
4．徐绪松，马莉莉，陈彦斌，中国上海股票市场GARCH效应的实证研究，武汉大学学报(理学版)2001．3
5．徐绪松，马莉莉，陈彦斌，R/S分析的理论基础：分数布朗运动，武汉大学学报(理学版)2003．5
6．徐绪松，熊保平，用RBF神经网络确定上海股市的分形维数，武汉大学学报(理学版)2003．3
7．徐绪松，杨小青，陈彦斌，半绝对离差证券组合投资模型，武汉大学学报，2002，48(3)
8．陈彦斌，金融市场中的混沌、分形及实证研究，硕士论文，2000
9．杨小青，中国股票市场混沌与分析研究，硕士论文，2003
10．王东生，曹磊，混沌、分形及其应用，中国科学技术大学出版社，1995
11．张尧庭，金融市场的统计分析，广西师范大学出版社，1998
12．李云，非线性动力系统的现代数学方法及其应用，人民交通出版社，1998
13．埃德加．E．彼得斯，资本市场的混沌与秩序，经济科学出版社，1999
14．埃德加．E．彼得斯，分形市场分析，经济科学出版社，2002
15．吕金虎、陆君安、陈士华，混沌时间序列分析及其应用，武汉大学出版社，2002
16．清源计算机工作室，Matlab基础及其应用，机械工业出版社，2000
17．徐龙炳，中国股票市场股票收益稳态特性的实证研究，金融研究，2001，第6期
18．伍海华，李道叶，资本市场有效性假定理论评述，东方论坛，2002，3
19．徐龙炳，陆蓉，有效市场理论的前沿研究，财经研究，2001，27(8)
20．高红兵，潘谨，陈宏民，深圳股票指数收益率序列的分形维，预测，2000，第6期
21．叶中行，杨利平，上证指数的混沌特性分析，上海交通大学学报，1998，32(3)
22．徐龙炳，陆蓉，探讨资本市场有效性的一种有效方法：分形市场，财经研究，1999，第1期
23．邓子来，胡健，市场有效理论及我国股票市场有效性的实证检验，金融论坛，2001，第10期
24．张维，黄兴，沪深股市的R/S实证分析，系统工程，2001．19(1)
25．王明涛，基于R/S法分析中国股票市场的非线性特征，预测，2002，21(3)
26．伍海华等，股票市场系统动力学分析：以上海股市为例，当代经济科学，2001，23(6)
27．魏巍贤，周晓明，中国股票市场波动的非线性GARCH预测模型，预测，1999，第5期
28．吴长凤，利用回归GARCH模型对我国沪深股市的分析，预测，1999，第4期
29．叶东毅等，径向基神经网络在股票走势模式分类中的应用，运筹与管理，1999，8(3)
30．李宗伟，王美娟，郑淑华，基于径向基神经网络的股价预测，上海理工大学学报，2002，24(1)
1. Abraham. The Individual Investor and the Weekend Effect. Journal of Financial and Quantitative Analysis, 29,1994
2. Campbell, J. Y., A. W. Lo, and A. C. MacKinlay, The Econometrics of Financial Markets Princeton University Press, Princeton, NJ, 1997.
3. Chi-fu Huang. Foundations for Financial Economics. New York: Elsevier Science Publishing Co., Inc., 1988.
4. Fama E F. Efficient Capital Market: a Review of Theory and Empirical Work. Journal of Finance, 1970.
5. Mandelbrot, B.B. When Can Price be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models. Review of Economics and Statistics, 1971.
6. Mandelbrot, B.B, Fractals&scaling infinance, spring-verlag New York, 1997
7. Mandelbrot B. The Variation of Certain Speculative Prices, Journal of Business, 36,1963
8. Engle, R. Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of UK inflation, Econometrica, 55,1987
9. Frank M.Z, Stengos T. Some Evidence Concerning Macroeconomic Chaos. Journal of monetary economics, 1988
10. Grassberger P, Procaccia I. Measuring the strangeness or strange attractors. Physica, 1983
11. Holger Kantz,Thomas Schreiber. Nonlinear time series analysis, Cambridge university press, 1977
12. Jim Lee. The Inflation and Output Variability Tradeoff: Evidence from α GARCH Model,
Economics Letters, 62,1999
13. N. H. Packard, J. P. Crutchfield, J. D. Farmer, and R. S. Shaw, Geometry from a Time Series, Phys. Rev. Let. 45, 1980
14. Peter S. Rose, Money and Capital Markets: Financial Institutions and Instruments in a Global Marketplace, McGraw-Hill Companies. Inc 6th edition, 1997
15. Wolf, etc,.Determining Lyapunov exponents from a times series, Physica D, 1985
16. Hurst.H.E, The Long-Term Storage Capacity of Reservoirs, Transactions of the American Society of Civil Engineer, 116,1951
17. William H Greene. Econometric Analysis. New Jersey: Prentice- Hall, Inc, 1993
18. Scheindman.J.A, Lebaron B. Nonlinear Dynamics and Stock Returns,The Journal of Business, 62,1989
19. Peters E E, Chaos and Order in the Capital Markets, New York: John Wiely&Sons, Inc., 1991
20. Takens F. Detection strange attractor in turbulence. Lecture Notes in Math, 1981
2．徐绪松，陈彦斌，深沪股市分形维实证研究，数量经济与技术经济研究，2000年11期
3．徐绪松，陈彦斌，深沪股票市场非线性实证研究，数量经济技术经济研究，2001年3期
4．徐绪松，马莉莉，陈彦斌，中国上海股票市场GARCH效应的实证研究，武汉大学学报(理学版)2001．3
5．徐绪松，马莉莉，陈彦斌，R/S分析的理论基础：分数布朗运动，武汉大学学报(理学版)2003．5
6．徐绪松，熊保平，用RBF神经网络确定上海股市的分形维数，武汉大学学报(理学版)2003．3
7．徐绪松，杨小青，陈彦斌，半绝对离差证券组合投资模型，武汉大学学报，2002，48(3)
8．陈彦斌，金融市场中的混沌、分形及实证研究，硕士论文，2000
9．杨小青，中国股票市场混沌与分析研究，硕士论文，2003
10．王东生，曹磊，混沌、分形及其应用，中国科学技术大学出版社，1995
11．张尧庭，金融市场的统计分析，广西师范大学出版社，1998
12．李云，非线性动力系统的现代数学方法及其应用，人民交通出版社，1998
13．埃德加．E．彼得斯，资本市场的混沌与秩序，经济科学出版社，1999
14．埃德加．E．彼得斯，分形市场分析，经济科学出版社，2002
15．吕金虎、陆君安、陈士华，混沌时间序列分析及其应用，武汉大学出版社，2002
16．清源计算机工作室，Matlab基础及其应用，机械工业出版社，2000
17．徐龙炳，中国股票市场股票收益稳态特性的实证研究，金融研究，2001，第6期
18．伍海华，李道叶，资本市场有效性假定理论评述，东方论坛，2002，3
19．徐龙炳，陆蓉，有效市场理论的前沿研究，财经研究，2001，27(8)
20．高红兵，潘谨，陈宏民，深圳股票指数收益率序列的分形维，预测，2000，第6期
21．叶中行，杨利平，上证指数的混沌特性分析，上海交通大学学报，1998，32(3)
22．徐龙炳，陆蓉，探讨资本市场有效性的一种有效方法：分形市场，财经研究，1999，第1期
23．邓子来，胡健，市场有效理论及我国股票市场有效性的实证检验，金融论坛，2001，第10期
24．张维，黄兴，沪深股市的R/S实证分析，系统工程，2001．19(1)
25．王明涛，基于R/S法分析中国股票市场的非线性特征，预测，2002，21(3)
26．伍海华等，股票市场系统动力学分析：以上海股市为例，当代经济科学，2001，23(6)
27．魏巍贤，周晓明，中国股票市场波动的非线性GARCH预测模型，预测，1999，第5期
28．吴长凤，利用回归GARCH模型对我国沪深股市的分析，预测，1999，第4期
29．叶东毅等，径向基神经网络在股票走势模式分类中的应用，运筹与管理，1999，8(3)
30．李宗伟，王美娟，郑淑华，基于径向基神经网络的股价预测，上海理工大学学报，2002，24(1)
1. Abraham. The Individual Investor and the Weekend Effect. Journal of Financial and Quantitative Analysis, 29,1994
2. Campbell, J. Y., A. W. Lo, and A. C. MacKinlay, The Econometrics of Financial Markets Princeton University Press, Princeton, NJ, 1997.
3. Chi-fu Huang. Foundations for Financial Economics. New York: Elsevier Science Publishing Co., Inc., 1988.
4. Fama E F. Efficient Capital Market: a Review of Theory and Empirical Work. Journal of Finance, 1970.
5. Mandelbrot, B.B. When Can Price be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models. Review of Economics and Statistics, 1971.
6. Mandelbrot, B.B, Fractals&scaling infinance, spring-verlag New York, 1997
7. Mandelbrot B. The Variation of Certain Speculative Prices, Journal of Business, 36,1963
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