In this paper we provide a detailed characterization of the asymptotic behavior of kernel density estimators for one-sided linear processes. The conjecture that asymptotic normality for the kernel density estimator holds under short-range dependence is proved under minimal assumptions on bandwidths. We also depict the dichotomous and trichotomous phenomena for various choices of bandwidths when the process is long-range dependent.
"Kernel density estimation for linear processes." Ann. Statist. 30 (5) 1441 - 1459, October 2002. https://doi.org/10.1214/aos/1035844982