Non-parametric Methods In Nonlinear Cointegration Time Series And Its Application

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.