Estimation of varying coefficient models with time trend and integrated regressors

In this paper we extend the semiparametric varying coefficient model to contain non-stationary I(1) and time trend as covariates. We show that the local constant kernel estimation method leads to a consistent estimation result. This is in contrast to the semiparametric varying coefficient model with stationary I(0) and time trend covariates where Liang and Li (2012) show that local constant estimation method leads to inconsistent estimation result. The extra variability of the I(1) regressor restore the consistency of the local constant estimation method. We derive the rate of convergence of the local constant estimators, simulations results strongly support our theoretical analysis.