Functional-coefficient models for nonstationary time series data

Abstract

This paper studies functional coefficient regression models with nonstationary time series data, allowing also for stationary covariates. A local linear fitting scheme is developed to estimate the coefficient functions. The asymptotic distributions of the estimators are obtained, showing different convergence rates for the stationary and nonstationary covariates. A two-stage approach is proposed to achieve estimation optimality in the sense of minimizing the asymptotic mean squared error. When the coefficient function is a function of a nonstationary variable, the new findings are that the asymptotic bias of its nonparametric estimator is the same as the stationary covariate case but convergence rate differs, and further, the asymptotic distribution is a mixed normal, associated with the local time of a standard Brownian motion. The asymptotic behavior at boundaries is also investigated.