Varying coefficient models for data with auto-correlated error process

The varying coefficient model has been popular in the literature. In this paper, we propose a profile least squares estimation procedure for its regression coefficients when the random error is an auto-regressive (AR) process. We study the asymptotic properties of the proposed procedure, and establish asymptotic normality for the resulting estimate. We show that the resulting estimate for the regression coefficients has the same asymptotic bias and variance as the local linear estimate for varying coefficient models with independent and identically distributed observations. We apply the SCAD variable selection procedure (Fan and Li (2001)) to reduce model complexity of the AR error process. Numerical comparison and finite sample performance of the resulting estimate are examined in Monte Carlo studies. Our simulation results demonstrate the proposed procedure is more efficient than the one ignoring the error correlation. The proposed methodology is illustrated by a data example.