资产价格易变性的非参数估计及其对中国股市的应用研究
|
摘要
由于金融资产价格的波动历来是金融体系风险积累的重要来源，几乎所有的金融危机都与金融资产价格的过度波动(Excessive Volatility)相关，因而判断和解释金融资产的波动性，也称为易变性(Volatility)，一直都是金融风险研究中的一个中心问题。
在本文中，我们把非参数回归的方法运用到我国实际的金融时间序列数据之中，讨论了我国股价指数收益率序列的易变性。而在用非参数回归进行估计时，选择合适的窗宽有着重要的意义。这是因为在理论上，如果缩小窗宽，偏差平方将会减少，方差将会增加，但是如果增大窗宽，方差虽会减少，偏差平方却会增加，因而每一个选择的规则都面临着在估计的方差和偏差的平方之间做出权衡，合适的窗宽应使得均方误差达到最小；在实践中，如果窗宽太小，随机性影响的增加会使非参数曲线估计呈现不规则形状，如果窗宽太大，则估计的函数将会受到过度平均的影响，其较细微的特征不易表现，因而窗宽的选择需要结合理论与实践经验。
我们依据运用交叉核实函数获取非参数回归核估计窗宽的原理，结合迭代累计平方和(ICSS)法则，于定理3．7中给出了一个获取窗宽的改良方法，并且在混合样本的情况下，利用我国实际的金融时间序列数据，对我国股价指数收益率序列的易变性进行了非参数回归核估计的实证分析；同时，我们在运用交叉核实函数获取非参数局部多项式估计的渐进最优窗宽，以及利用迭代累计平方和(ICSS)法则确定了多项式的阶数以后，将局部多项式估计的方法对我国股价指数收益率序列的易变性进行了较为深入地研究和分析，并与非参数回归核估计的结果进行了比较。
四川大学硕士学位论文
文章是这样安排的:我们在第一章中引入了金融时间序列易变性的异方
差模型;在第二章中介绍了非参数回归估计方法及一些预备知识;在第三章
中讨论了资产价格易变性的非参数核估计方法;在第四章中讨论了资产价格
易变性的局部多项式估计方法;在第五章中我们对中国股价指数收益率序列
的易变性进行了非参数的估计，获得了一些有意义的结论。
Because the volatility of asset price comes from the accumulation of the risk in finance system and almost all financial crises are related to excessive volatility of asset price, juding and explaining the volatility is always one of the focuses in financial risk study.
In this paper, we use nonparametric regression method in Chinese financial time series, we also use both kernel regression after improving cross-validation function and local polynomial estimation of regression under mixing condition to study and analyze the volatility in Chinese stock market. This paper is arranged as follows: in chapter one, we introduce the volatility model of heteroscedasticity in financial time series; in chapter two, we introduce some preliminary knowledge; in chapter three, nonparametric kernel estimation is discussed in the respects of bandwidth selection, consistency and normality of estimator; in chapter four, local polynomial regression estimation is also discussed; at last, we estimate the volatility of Chinese stock market with these methods and conclude some interesting results in chapter five.
在本文中，我们把非参数回归的方法运用到我国实际的金融时间序列数据之中，讨论了我国股价指数收益率序列的易变性。而在用非参数回归进行估计时，选择合适的窗宽有着重要的意义。这是因为在理论上，如果缩小窗宽，偏差平方将会减少，方差将会增加，但是如果增大窗宽，方差虽会减少，偏差平方却会增加，因而每一个选择的规则都面临着在估计的方差和偏差的平方之间做出权衡，合适的窗宽应使得均方误差达到最小；在实践中，如果窗宽太小，随机性影响的增加会使非参数曲线估计呈现不规则形状，如果窗宽太大，则估计的函数将会受到过度平均的影响，其较细微的特征不易表现，因而窗宽的选择需要结合理论与实践经验。
我们依据运用交叉核实函数获取非参数回归核估计窗宽的原理，结合迭代累计平方和(ICSS)法则，于定理3．7中给出了一个获取窗宽的改良方法，并且在混合样本的情况下，利用我国实际的金融时间序列数据，对我国股价指数收益率序列的易变性进行了非参数回归核估计的实证分析；同时，我们在运用交叉核实函数获取非参数局部多项式估计的渐进最优窗宽，以及利用迭代累计平方和(ICSS)法则确定了多项式的阶数以后，将局部多项式估计的方法对我国股价指数收益率序列的易变性进行了较为深入地研究和分析，并与非参数回归核估计的结果进行了比较。
四川大学硕士学位论文
文章是这样安排的:我们在第一章中引入了金融时间序列易变性的异方
差模型;在第二章中介绍了非参数回归估计方法及一些预备知识;在第三章
中讨论了资产价格易变性的非参数核估计方法;在第四章中讨论了资产价格
易变性的局部多项式估计方法;在第五章中我们对中国股价指数收益率序列
的易变性进行了非参数的估计，获得了一些有意义的结论。
Because the volatility of asset price comes from the accumulation of the risk in finance system and almost all financial crises are related to excessive volatility of asset price, juding and explaining the volatility is always one of the focuses in financial risk study.
In this paper, we use nonparametric regression method in Chinese financial time series, we also use both kernel regression after improving cross-validation function and local polynomial estimation of regression under mixing condition to study and analyze the volatility in Chinese stock market. This paper is arranged as follows: in chapter one, we introduce the volatility model of heteroscedasticity in financial time series; in chapter two, we introduce some preliminary knowledge; in chapter three, nonparametric kernel estimation is discussed in the respects of bandwidth selection, consistency and normality of estimator; in chapter four, local polynomial regression estimation is also discussed; at last, we estimate the volatility of Chinese stock market with these methods and conclude some interesting results in chapter five.
引文
[1] (英)格利滋著．唐旭等译．金融工程学．北京，经济科学出版社．1998．
[2] Barchelier,L. Théorie de la speculation. Annales scientifiques de 1'école normale supérieure. 1900.17.21-88
[3] Fama,E. The Behavior of Stock Market Prices. Journal of Business.1965.38.34-105
[4] Shiller,R. Do Stock Prices Move too much to be Justified by Subsequent Changes in Dividends? American Economic Review. 1981.71.421
[5] Engle,R.F. Autoregressive Conditional Heteroscedasticity with Estimators of the Variance of United Kindom Inflation. Econometrica. 1981.50.987-1008
[6] Bollerslev,T. Generalized Autoregressive Conditional Heteroscedasticity. Journal of Econometrics. 1986.31.307-327
[7] Jiangang Xu. Modeling Shanghai Stock Market Volatility. Annals of Operation Research. 1999.97.141-152
[8] 王军波，邓述慧．利率成交量对股价波动的影响—GARCH修正模型的应用．系统工程理论与实践．1999(9)：49-57
[9] 陈泽忠，杨启智，胡金泉．中国股票市场的波动性研究—EGARCH-M模型的应用．决策借鉴．2000(10)：24-27
[10] 唐齐鸣，陈健．中国股市的ARCH效应分析．世界经济．2001(3)：29-36
[11] YIN-HUA YEH,TSUN-SIOU LEE,JEN-FU PEN. Stock Returns and Volatility under Market Segmention:The Case of Chinese A and B Shares. Review of Quantitative Finance and Accounting. 2002.18.239-257
[12] 胡海鹏，方兆本．用AR-EGARCH-M模型对中国股市波动性的拟合分析．系统工程．2002(7)：31-36
[13] Heid,F. Nonparametric Volatility Estimation of Exchange Rates and Stock Prices. Discussion Paper A-533,Sonderforschungsbereich 303.University of Bonn.1996.
[14] Heid,F. Estimating the Functional Components of Asset Price Volatilities. Discussion Paper A-565,Sonderforschungsbereich 303.University of Bonn.1997.
[15] 陆传荣，林正炎．混合相依变量的极限理论．北京：科学出版社．1997．
[16] Nadaraya,E. On Estimating Regression. Theory of Probability and Its Applications. 1964.10.186-190
[17] Watson,G. Smooth Regression Analysis. Sankhya,Series A. 1964.26.359-372
[18] Bierens,H. Uniform Consistency of Kernel Estimators of a Regression Function under Generalized Conditions. Journal of the American Statistical Association. 1983.78.254-286
[19] 柴根象．相依样本分布函数、回归函数的非参数估计的强相合性．系统科学与数学．1988(3)：281-288
[20] Robinson,P. Nonparametric Estimators for Time Series. Journal of Time Series Analysis. 1983.4.185-197
[21] Shibata,R. An Optimal Selection of Regression Variables. Biometrica. 1981.68.45-54
[22] Gyrfi,L.,Hrdle,W.,Sarda and Vieu,P. Nonparmetric Curve Estimation from Time Series,No.60 in Lecture Notes in Statistics.Springer Verlag.1989.
[23] Hrdle,W. and Marron,J. Optimal Bandwidth Selection in Nonparametric Regression Function Estimation.The Annals of Statistics. 1986.13.1465-1481
[24] Inclán,C. and G.C.Tiao. Use of Cumulative Sums of Squares for Restrospective Detection of Changes of Variance. Journal of the American Statistical Association.994.89.913-923
[25] Fan,J. and Gijbels,I. Local Polynomial Modelling and Its Applications. Chapman and Hall. 1996.
[26] Masry, E. and Fan,J. Local Polynomial Estimation of Regression Functions for Mixing Processes. Scandinavian Journal of Statistics.997.24.165-179
[27] 李子奈，叶阿忠．高等计量经济学．北京：清华大学出版社．2000．
[28] Hrdle,W. Applied Nonparametric Regression. Cambridge University Press.1990.
[29] B. L. S. Prakasa Rao. Nonparametric Functional Estimation. Academic Press. (London)LTD. 1983.
[2] Barchelier,L. Théorie de la speculation. Annales scientifiques de 1'école normale supérieure. 1900.17.21-88
[3] Fama,E. The Behavior of Stock Market Prices. Journal of Business.1965.38.34-105
[4] Shiller,R. Do Stock Prices Move too much to be Justified by Subsequent Changes in Dividends? American Economic Review. 1981.71.421
[5] Engle,R.F. Autoregressive Conditional Heteroscedasticity with Estimators of the Variance of United Kindom Inflation. Econometrica. 1981.50.987-1008
[6] Bollerslev,T. Generalized Autoregressive Conditional Heteroscedasticity. Journal of Econometrics. 1986.31.307-327
[7] Jiangang Xu. Modeling Shanghai Stock Market Volatility. Annals of Operation Research. 1999.97.141-152
[8] 王军波，邓述慧．利率成交量对股价波动的影响—GARCH修正模型的应用．系统工程理论与实践．1999(9)：49-57
[9] 陈泽忠，杨启智，胡金泉．中国股票市场的波动性研究—EGARCH-M模型的应用．决策借鉴．2000(10)：24-27
[10] 唐齐鸣，陈健．中国股市的ARCH效应分析．世界经济．2001(3)：29-36
[11] YIN-HUA YEH,TSUN-SIOU LEE,JEN-FU PEN. Stock Returns and Volatility under Market Segmention:The Case of Chinese A and B Shares. Review of Quantitative Finance and Accounting. 2002.18.239-257
[12] 胡海鹏，方兆本．用AR-EGARCH-M模型对中国股市波动性的拟合分析．系统工程．2002(7)：31-36
[13] Heid,F. Nonparametric Volatility Estimation of Exchange Rates and Stock Prices. Discussion Paper A-533,Sonderforschungsbereich 303.University of Bonn.1996.
[14] Heid,F. Estimating the Functional Components of Asset Price Volatilities. Discussion Paper A-565,Sonderforschungsbereich 303.University of Bonn.1997.
[15] 陆传荣，林正炎．混合相依变量的极限理论．北京：科学出版社．1997．
[16] Nadaraya,E. On Estimating Regression. Theory of Probability and Its Applications. 1964.10.186-190
[17] Watson,G. Smooth Regression Analysis. Sankhya,Series A. 1964.26.359-372
[18] Bierens,H. Uniform Consistency of Kernel Estimators of a Regression Function under Generalized Conditions. Journal of the American Statistical Association. 1983.78.254-286
[19] 柴根象．相依样本分布函数、回归函数的非参数估计的强相合性．系统科学与数学．1988(3)：281-288
[20] Robinson,P. Nonparametric Estimators for Time Series. Journal of Time Series Analysis. 1983.4.185-197
[21] Shibata,R. An Optimal Selection of Regression Variables. Biometrica. 1981.68.45-54
[22] Gyrfi,L.,Hrdle,W.,Sarda and Vieu,P. Nonparmetric Curve Estimation from Time Series,No.60 in Lecture Notes in Statistics.Springer Verlag.1989.
[23] Hrdle,W. and Marron,J. Optimal Bandwidth Selection in Nonparametric Regression Function Estimation.The Annals of Statistics. 1986.13.1465-1481
[24] Inclán,C. and G.C.Tiao. Use of Cumulative Sums of Squares for Restrospective Detection of Changes of Variance. Journal of the American Statistical Association.994.89.913-923
[25] Fan,J. and Gijbels,I. Local Polynomial Modelling and Its Applications. Chapman and Hall. 1996.
[26] Masry, E. and Fan,J. Local Polynomial Estimation of Regression Functions for Mixing Processes. Scandinavian Journal of Statistics.997.24.165-179
[27] 李子奈，叶阿忠．高等计量经济学．北京：清华大学出版社．2000．
[28] Hrdle,W. Applied Nonparametric Regression. Cambridge University Press.1990.
[29] B. L. S. Prakasa Rao. Nonparametric Functional Estimation. Academic Press. (London)LTD. 1983.