非参数协整和误差修正模型及其在金融中的应用
Applications of Nonparametric Cointegration and Error Correction Model to Finance
摘要: 本文主要研究了协整理论和非线性协整的非参数方法两个领域，包括线性协整及线性误差修正模型，非线性协整及非线性误差修正模型，ACE算法和局部多项式回归方法，基本梳理清楚了该领域的研究脉络和框架。本文运用Matlab编程实现了局部多项式回归这一非参数检验方法，详细地梳理了协整理论的内容，包括线性协整理论、线性误差修正模型、线性协整理论的估计和检验、非线性协整和误差修正模型及其估计和检验，并且对个中细节进行了注解，使脉络更为清晰明了，从而增进协整理论的易读性。对时间序列协整的非线性存在的应用提出了新的方法，即融合岭回归的局部多项式回归的非参数方法，通过仿真表明，该方法有很好的估计效果。选取日本、新加坡、台湾三地指数数据进行实证分析，把局部多项式回归的非参数方法和协整、误差修正模型结合，实现了对协整、误差修正模型的估计，并且得到了较高模型估计精度，尤其重要的是，能够合理地解释局部多项式回归这一非参数方法的一阶导数在日本、新加坡、台湾三地股市指数中的意义。
Abstract: This paper mainly focuses on co-integration theory and nonparametric method with nonlinear co-integration, which includes linear co-integration and linear error correction model, nonlinear co-integration and nonlinear error correction model, the ACE algorithm and local polynomial regression. It is clearly proved right by these analytical methods. The Matlab programming is fully exerted to realize the local polynomial regression, a nonparametric test method. In this paper, co-integration theory is clarified in details including linear theory of co-integration, linear estimation of error correction model, linear co-integration theory and tests, the nonlinear co-integration and error correction model as well as the estimation and inspection towards it. Moreover, the annotation is added for individual specifics, aiming to clarify the structures of co-integration. The existing application of time series nonlinear co-integration is put forward to serve the new method, namely the method of fusing the ridge regression nonparametric local polynomial regression. The simulation shows that this method is proved to be right. The index data assisting the researcher access to the empirical analysis are references from Japan, Singapore and Taiwan. It is on its purpose by combing the non-parametric method of local polynomial regression, co-integration and error correction model to estimate the analysis on the co-integration and error correction model. The precision of the model is assured. The local polynomial regression can be aimed to assist in explaining the significance of the non-parametric method of first derivative stock indexes in Japan, Singapore and Taiwan.
文章引用：殷俊, 苏理云, 周甲凯, 何雄飞, 李泓强, 彭相武. 非参数协整和误差修正模型及其在金融中的应用[J]. 金融, 2014, 4(1): 1-8. http://dx.doi.org/10.12677/FIN.2014.41001

参考文献

[1] Granger, C.W.J. (1981) Some properties of time series data and their use in econometric model specification. Journal of Econo-metrics, 16, 121-130.
[2] Engle R.F., Granger C. W. J. (1987) Cointegration and error correction: Representation, estimation, and testing. Econometrical, 55, 251-276.
[3] 樊智, 张世英 (2005) 非线性协整建模研究及沪深股市实证分析. 管理科学学报, 1, 73-77.
[4] 刘丹红, 张世英 (2006) 基于小波神经网络的非线性误差校正模型及其预测. 控制与决策, 10, 1114-1118.
[5] Sargan, J.D. (1964) Wages and prices in the United Kingdom: A study in econometric methodology. In: Hart, P.E., Mills, G. and Whitacker, J.K., Eds., Econometric Analysis for National Economic Planning, Butterworths, London, 34-36.
[6] Anderson H. and Berra P. (1977) Minimum cost selection of secondary indexes for formatted files. ACM Transactions on Database Systems, 2, 68-90.
[7] Davidson (1987) Asymptotic properties of least squares estimators of cointegrating vectors. Econometrica: Journal of the Econometric Society, 55, 1035-1056.
[8] Stock J.H. and Watson, M.W. (1988) A simple estimator of cointegrating vectors in higher order integrated systems. Econometrica, 61, 783-820.
[9] Dickey, D.A. and Fuller, W.A. (1979) Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74, 427-431
[10] Dickey, D.A. and Fuller, W.A. (1981) Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica, 49, 1057-1072.
[11] 魏巍贤 (1997) 非平稳时间序列预测组合的条件. 预测, 4, 47-49.
[12] 张丽杰 (2006) 辽宁省对外贸易与经济增长的协整及因果关系检验. 统计教育, 3, 53-55.
[13] 江孝感, 王利, 朱涛 (2008) 向量金融时间序列协整与协同持续关系——基于理论的思考. 管理工程学报, 1, 78-81.
[14] Karlsen, H.A., Myklebust, T. and Tjøstheim, D. (2007) Nonparametric estimation in a nonlinear cointegration model. The Annals of Statistics, 35, 252-299.
[15] Schienle, M. (2008) Nonparametric nonstationary regression. Doctoral Thesis, Mannheim University, Mannheim.
[16] Wang, Q.Y. and Phillips, P.C.B. (2009) Asymptotic theory for local time density estimation and nonparametric cointegrating regression. Econometric Theory, 25, 710-738.
[17] 张喜彬, 孙青华, 张世英 (1999) 非线性协整关系及其检验方法研究. 系统工程学报, 1, 57-68.
[18] 孙青华, 张喜彬, 张世英 (2000) 非线性协整关系的存在性研究. 管理科学学报, 3, 65-74.
[19] 程细玉, 张世英 (2001) 向量分整序列的非线性协整研究. 系统工程理论方法应用, 1, 85-87.
[20] 孙青华, 张世英 (2002) 长记忆向量时间序列的非线性协整关系研究. 天津大学学报, 3, 327-331.
[21] Fan, J. and Gijbels, I. (1995) Data-driven bandwidth selection in local polynomial fitting: variable bandwidth and spatial adaptation. Journal of the Royal Statistical Society, Series B, 57, 371394.
[22] Takeda, H., Farsiu, S. and Milanfar, P. (2006) Robust kernel regression for restoration and reconstruction of images from spares noisy data. Process of the International Conference on Image Processing, 24, 1257-1260.
[23] He, Q.X. and Zheng, M. (2003) Local polynomial regression for heteroscedaticity in the simple linear model. Systems Engineering-Theory Methodology Applications, 12, 153-156.
[24] Su, L.Y. and Li, F.L. (2010) Deconvolution of defocused image with multivariate local polynomial regression and iterative wiener filtering in DWT domain. Mathematical Problems in Engineering, Article ID: 605214, 14 Pages.
[25] Su, L.Y. (2010) Prediction of multivariate chaotic time series with local polynomial fitting. Computers & Mathematics with Applications, 59, 737-744.
[26] Su, L.Y. (2011) Multivariate local polynomial estimation with application to Shenzhen component index. Discrete Dynamics in Nature and Society, 2011, 1-11.
[27] http://www.resset.com/cn/

为你推荐