  In this paper, we study nonparametric models allowing for locally stationary
regressors and a regression function that changes smoothly over time. These
models are a natural extension of time series models with time-varying
coefficients. We introduce a kernel-based method to estimate the time-varying
regression function and provide asymptotic theory for our estimates. Moreover,
we show that the main conditions of the theory are satisfied for a large class
of nonlinear autoregressive processes with a time-varying regression function.
Finally, we examine structured models where the regression function splits up
into time-varying additive components. As will be seen, estimation in these
models does not suffer from the curse of dimensionality.
