Uniformly root-n consistent density estimators for weakly dependent invertible linear processes

Abstract

Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate n^−1/2. Our estimator is a convolution of two different residual-based kernel estimators. We obtain in particular convergence rates for such residual-based kernel estimators; these results are of independent interest.