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.