【作者】 舒晓惠；

【导师】 雷钦礼；

【作者基本信息】 暨南大学 ， 数量经济学， 2010， 博士

【摘要】 本文主要研究了非线性协整理论的非参数检验与估计两个领域,包括非线性存在性,混沌与分形特征,非线性非平稳检验以及非线性协整检验与估计。基本梳理清楚了这两个领域的研究脉络和框架。本文运用Gauss编程实现了所提各种非参数检验方法,MC仿真给出了相关统计量的临界值表,并比较了各方法的优劣。在随后的实证研究中,本文对我国货币各变量序列,以及我国与国际股市指数序列应用所给出的非线性协整理论的非参数方法进行了非线性存在性检验,混沌与分形特征检验,存在非线性的非平稳检验以及非线性协整检验与估计,得出了较此前学者们应用线性协整理论相关方法更一般的结论。综合看,本文主要在如下几个方面做了开拓性研究：第一,较为详细地梳理了线性协整理论的内容,对个中细节进行了注解,使得理论脉络更为清晰明了,从而增进了协整理论的易读性。第二,对线性加强型神经网络在时间序列的非线性存在性检验中的应用提出了新的方法,即加强型小波神经网络并给出了新的实现算法：改进的带动量的LM算法。MC仿真表明,高斯小波、墨西哥帽小波等两线性加强型小波神经网络方法效果较好。第三,发现应用小数据量法实现的最大Lyapunov指数值的意义在随机条件下和确定性混沌条件下是不一致的。因此,利用最大Lyapunov指数探讨非线性协整尚需商榷。第四,发展了秩检验方法,推导了其分布,针对非高斯的单峰分布和存在序列相关性问题提出了相应的改进方法和实现方法,即基于Bootstrap和Block Bootstrap抽样的单位根逆得分秩检验方法。第五,给出了协整的秩检验方法和记录数检验方法的检验临界值表和响应面函数,并应用上述方法对中国与世界主要证券市场股指进行了实证分析,发现其更多存在的是非线性协整关系。第六,研究了三种神经网络应用于非线性协整理论的可行性,比较了其优劣,特别地,提出了带动量改进的LM算法的小波神经网络,使得其更具泛化能力。另外,本文还提出应用加强型神经网络对非线性非平稳时间序列进行滤波,其更适用于非线性的情形。更多还原

【Abstract】 This paper studied two areas of non-parametric testing and estimating methods in nonlinear cointegration theory including non-linear existence, Chaos and Fractal, nonlinear non-stationary test, and nonlinear cointegration test and estimation; clearly distinguished the basic research context and framework. Then realized various non-parametric test methods proposed in this paper by Gauss programming and given the threshold table of related statistics, compared the pros and cons of each methods by MC simulation methods. In this paper, the subsequent empirical study was researched on the variables of currency, China and the international stock market index. Using the non-parametric methods of nonlinear Cointegration theory, the sequence tests was given including testing the existence of nonlinear, the chaotic and fractal characteristics, the nonlinear non-stationary and the nonlinear cointegration, then the estimation of the nonlinear cointegration was discussed. Therefore, got more general conclusion related to linear cointegration theory. Comprehensive view, this paper has done in the following pioneering research:Firstly, a more detailed sort of linear cointegration theory for the contents was given, some details was Noted, which makes the context more explicit, thus enhanced the accessibility.Secondly, presented a new method, namely, the enhanced linear wavelet neural network, which in the application of testing the presence of nonlinear time series, and gave a new realization algorithm:the improved momentum LM algorithm. MC simulation showed that the method of Gauss and Mexico Cap WNN had good power.Thirdly, found that the meaning of maximum Lyapunov index value achieved by the small-data method was inconsistent under conditions of random and deterministic chaos. Therefore, using the maximum Lyapunov index of nonlinear cointegration still needed discussion.Fourthly, developed the rank test method for non-Gaussian single-peak distribution and the presence of serial correlation, put forward the improved method and implementation method, that is, the Unit Root Inverse-score rank test which based on Bootstrap and Block Bootstrap sampling.Fifthly, given the threshold table and response surface function of the rank cointegration test and the record counting cointegration Test. And applied those methods in China and the world’s major stock market indexes, empirical analysis found that there were more nonlinear cointegration.Sixthly, the feasibility of three neural network methods applied for nonlinear cointegration was studied, and their advantages and disadvantages were compared. in particular, proposed the wavelet neural network with improved momentum LM algorithm, making it more generalization. In addition, the paper also proposed the application of enhanced neural network for filtering nonlinear non-stationary time series, which was more suitable for nonlinear situations.更多还原