Two-step estimation of time-varying additive model for locally stationary time series

In the analysis of locally stationary process, a time-varying additive model (tvAM) can effectively capture the dynamic feature of regression function. In combination with the strengths of tensor product of B-spline smoothing and local linear smoothing method, a two-step estimation method is proposed. It is shown that the proposed estimator is uniformly consistent and asymptotically oracle efficient as if the other component functions were known. Furthermore, a nonparametric bootstrap procedure is proposed to test the time-varying property of regression function. Simulation studies investigate the finite-sample performance of the proposed methods and validate the asymptotic theory. An environmental dataset illustrating the proposed method is also considered.