A two-stage approach to additive time series models

For nonlinear additive time series models, an appealing approach used in the literature to estimate the nonparametric additive components is the projection method. In this paper, it is demonstrated that the projection method might not be efficient in an asymptotic sense. To estimate additive components efficiently, a two-stage approach is proposed together with a local linear fitting and a new bandwidth selector based on the nonparametric version of the Akaike information criterion. It is shown that the two-stage method not only achieves efficiency but also makes bandwidth selection relatively easier. Also, the asymptotic normality of the resulting estimator is established. A small simulation study is carried out to illustrate the proposed methodology and the two-stage approach is applied to a real example from econometrics.