The Application And The Empirical Research Of The Tail Regression Based On Cavar Model

Heavy tail exists in most of the time series data so frequently that it is insufficient to distribute data by the normal distribution merely.The probability of heavy tail is higher than normal hypothesis in time series data.If we can not take this phenomenon into account,it would have a impact on the data regression simulation accuracy even leading to make some decision-making errors.As well as in many regression models based on time series,the least squares is the most common way to estimate the parameters which is easily affected by the extreme value as the result of the depressed regression model veracity,because the assumptions of the method in many cases are not easy to meet.In a portfolio,it was approved to adopted CVaR model to estimate losses which regards one of the condition loss belong to tail as the objective factor what we would used to estimate the parameters in this article.The researching point of this article is to establish a regression model for time series mainly in order to achieve the forecast of future time.On the basis of the principle "Taylor formula",any complex sufficiently smooth function can be expressed as a polynomial form.As a result,this paper just gives a multivariate implicit function in the first place as an example to construct its loss function,and then structuring CVaR model based on the distribution of the loss function for continuous and discrete value respectively and changes its form as solving a goal programming.In the end,we take the China's foreign trade data for example to establish linear and nonlinear time series model whose parameters are estimated by CVaR model and least squares method and we consider the residual value as the testing standard of the regression accuracy.Finally we get the following conclusions: 1.The regression model accuracy based on CVaR method is higher than that of least squares regression method especially with more significant tail data.2.Nonlinear model can grasp the overall characteristics of time series data compared with the linear regression model.3.we can get a more accurate assessment of the current development situation and work outthe corresponding trade policy on the strength of the forecast of the total amount of China's foreign import and export trade volume by the established model.