Semiparametric estimation of regression functions in autoregressive models

This paper proposes a semiparametric method for an autoregressive model by combining a parametric regression estimator with a nonparametric adjustment. The regression has a parametric framework. After the parameter is estimated through a general parametric method, the obtained regression function is adjusted by a nonparametric factor, and the nonparametric factor is obtained through a natural consideration of the local L2-fitting criterion. Some asymptotic and simulation results for the semiparametric method are discussed.