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.
"Uniformly root-n consistent density estimators for weakly dependent invertible linear processes." Ann. Statist. 35 (2) 815 - 843, April 2007. https://doi.org/10.1214/009053606000001352