The Nonparametric Cointegration And Error Correction Model And Their Applications In Finance

In this paper, two fields have been studied, that is, the cointegration theory andnonparametric methods of nonlinear cointegration, in which include linear and non-linearcointegration and linear error correction model, the ACE-algorithms and local polynomialregression method. The nonparametric method of local polynomial regression has beenrealized by Matlab programming. In the following empirical analysis, based on thecointegration analysis theory, the conclusion is that there is a long-term stable relationshipbetween Shanghai, Shenzhen and Hong Kong stock index data. However, Granger causalitytest shows that the Shanghai and Shenzhen index were not the reason of Hong Kong index.Based on the conclusion above, a improved method of local polynomial regression has beenproposed. The ridge regression theory has been used in this method, and it can approximatethe nonlinear cointegration function, by which can get the derivative values of Hang Sengindex to Shanghai and Shenzhen index, respectively. Furthermore, the impact of Shanghai andShenzhen index on the Hang Seng Index can be obtained by observing the partial derivatives.In empirical analysis, there is a non-linear relationship between Shanghai-Shenzhen and HongKong stock market. This paper mainly research in the following several aspects:First, the context of cointegration theory has been clearly organized in detail, includinglinear cointegration theory and its error correction model and estimation and test, nonlinearcointegration and error correction model, estimation and their test. Besides, the details arenoted, then the context is clearer, and the cointegration theory is more easily to understand.Second, a new method for the application in nonlinear time series cointegration has beenproposed, that is, nonparametric method of local polynomial regression of ridge regression.Simulation results show that this method has a good estimation effect.Third, the empirical analysis based on the Shanghai, Zhenzhen and Hong Kong stockindex data has been carried out, combining cointegration, error correction model with localpolynomial regression method. The estimation of cointegration, error correction model isrealized, and get a higher estimated accuracy. It is particularly important that it can reasonablyexplain the significance of first-order derivative of local polynomial regression ofnonparametric method in Shanghai, Zhenzhen and Hong Kong stock market index.