Functional-Coefficient Models for Nonstationary Time Series Data∗

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. Consistency and 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. When the coefficient function is a function of a nonstationary variable, the new findings are that asymptotic bias is the same as stationarity covariate case but convergence rate differs, and further, the asymptotic distribution is mixed normal, associated with the local time of a standard Brownian motion. Asymptotic behavior at boundaries is also investigated.