Research On Predictive Methods Of Non-parametric Regression Model Under Several Errors

In time series data analysis,since the structure that many actual data has unknown or the nonlinear trend is difficult to determine,and the error structure may be heteroscedastic and dependent relationships,it is difficult to ordinaryly analyze these complicated data.In this paper,I focus on the prediction methods of nonparametric regression model under several complex errors.The nonparametric regression models considered include four errors,i.e.: MA model and ARMA model under homoscedasticity,and MA model and ARMA model under heteroscedasticity.Based on the polynomial spline method and the criteria of mean square error(MSE)and mean absolute error(MAE),a suitable prediction method is selected from the three methods,non-extrapolation method,linear extrapolation method and nonlinear extrapolation method,through Monte Carlo simulation and empirical analysis.The specific content and main results are as follows.(1)Residual MA model under homoskedasticity.In the simulation example,extrapolation methods are superior to non-extrapolation method in the view of MSE and MAE,overall.The order of the merits of these prediction methods is linear extrapolation method,nonlinear extrapolation method and non-extrapolation method.In the empirical analysis of the fitting and forecasting for the composition of sector added value-added value of financial industry,the results are similar to those in the simulation example.(2)Residual ARMA model under homoskedasticity.In the view of MSE and MAE,the simulation example shows that the fitting performance has thin advantage.However,the order of the merits of these prediction methods is linear extrapolation method,nonlinear extrapolation method and non-extrapolation method.In the empirical analysis of the fitting and forecasting for Per capita GDP index,the results are similar to those in the simulation example.(3)Residual MA model under heteroscedasticity.The simulation example shows extrapolation methods are superior to non-extrapolation method in the view of MSE and MAE,overall.The order of the merits of these prediction methods is linear extrapolation method,nonlinear extrapolation method and non-extrapolation method.The empirical analysis of the fitting and forecasting of the Per Capita GDP Index of Chongqing shows that the fitting performance has thin advantage.However,the prediction performance has the similar results as the simulation example.(4)Residual ARMA model under heteroscedasticity.In the simulation example,the fitting performance of the extrapolation method has thin advantage,and the order of the merits of these prediction methods is linear extrapolation method,nonlinear extrapolation method and non-extrapolation method.The empirical analysis of the fitting and forecasting of the capita GDP index shows the similar results as the simulation example.In a word,the linear extrapolation is a better predition method,which is suggested to use in model prediction.