Efficient estimation of varying coefficient models with serially correlated errors

•A new estimation method is proposed for VCM with serially correlated errors.•The proposed estimator is more efficient than the existing local linear estimator.•A procedure is suggested to select the order of the AR error process.•Simulation results show that significant gains can be achieved with our method.•A real example is given to show the usefulness of the proposed estimation method.

The varying coefficient model provides a useful tool for statistical modeling. In this paper, we propose a new procedure for more efficient estimation of its coefficient functions when its errors are serially correlated and modeled as an autoregressive (AR) process. We establish the asymptotic distribution of the proposed estimator and show that it is more efficient than the conventional local linear estimator. Furthermore, we suggest a penalized profile least squares method with the smoothly clipped absolute deviation (SCAD) penalty function to select the order of the AR error process. Simulation evidence shows that significant gains can be achieved in finite samples with the proposed estimation procedure. Moreover, a real data example is given to illustrate the usefulness of the proposed estimation procedure.