Research On Nonlinear Structure Of ARCH Model

With the rapid development of China's securities and stocks market,uncertainty and empirical analysis of the stock market price c hanges has become one of the core problems of modern financial research.It is very important to describe and predict the objective economic process with time series models.During the process of securities investment,people often establish and apply the relevant model to analysis stock market systematically.In the last some years ARCH model with a very rapid development has been widely used to verify the regularity of financial theory,to describe financial markets and to make decision and forecast financial markets' changes.However,in practical application,a large amount of financial data emerged nonlinear characteristics,such as non-normal,asymmetric cycle,bimodal shape,and heteroscedasticity between the variables and the like.Therefore,the traditional the linear ARCH model with parameters often leads to relatively large error in modeling model.But the non-parametric model can't provide for specific forms of model,so we propose a new nonlinear ARCH models.This non-linear ARCH model is based on GMDH method to be established,which don't only portray non-linear characteristics of financial data,but also can give a specific form of the model,the most important its the prediction accuracy is better.This paper is expected that this method of GMDH will to be introduced in conditional variance of ARCH model,and the nonlinear ARCH model based on GMDH method will be applied to Empirical research in the daily yield rate and earnings per 5 minutes of Shanghai Composite Index and Shenzhen Component Index.We concluded that:1.For the volatility of the Shanghai Composite Index and Shenzhen Component Index,The nonlinear ARCH model based on GMDH method predicted the better results and estimate higher accuracy than the traditional linear ARCH model.2.Based on the GMDH method,nonlinear ARCH model,which has been added Investor Sentiment Index,estimates better accuracy and higher predictions than that nonlinear ARCH models are not added to Investor Sentiment Index.3.Overall,The ARCH model based on GMDH method,the resulting of Mean Square Error and Mean Absolute Error are smaller.4.This article will describe the earnings volatility of the Shanghai Composite Index and Shenzhen Component Index with the nonlinear ARCH model based on GMDH method,and objectively findings and recommendations are given.This paper provides a good thought for the study on volatility of financial assets in the future,which will apply the nonlinear ARCH model based on GMDH neural network method.