A Semiparametric Estimation for the First-Order Nonlinear Autoregressive Time Series Model with Independent and Dependent Errors

摘要

In this paper, the first-order nonlinear autoregressive model is considered and a semiparametric method is proposed to estimate nonlinear regression function for both independent and dependent errors. We use Taylor series expansion which has a parametric framework as a representation of the nonlinear regression function. The least squares method is used for parametric estimation, and then, the obtained nonlinear regression function is adjusted by a nonparametric factor. The nonparametric kernel approach is applied to estimate this nonparametric factor. Some consistency properties and simulated results for the semiparametric estimators in a nonlinear autoregressive function are presented. MSE and AIC criterions are also applied to verify the efficiency of the proposed model. A real data on the sale of fresh foods in New Zealand are analyzed to illustrate the application of the proposed semiparametric method.