Kernel estimation for time series: An asymptotic theory

Abstract

We consider kernel density and regression estimation for a wide class of nonlinear time series models. Asymptotic normality and uniform rates of convergence of kernel estimators are established under mild regularity conditions. Our theory is developed under the new framework of predictive dependence measures which are directly based on the data-generating mechanisms of the underlying processes. The imposed conditions are different from the classical strong mixing conditions and they are related to the sensitivity measure in the prediction theory of nonlinear time series.