Estimation of the Asymptotic Variance of Kernel Density Estimators for Continuous Time Processes

In order to construct confidence sets for a marginal density f of a strictly stationary continuous time process observed over the time interval [0, T], it is necessary to have at one's disposal a Central Limit Theorem for the kernel density estimator fT. In this paper we address the question of nonparametric estimation of the asymptotic variance of  fT, an unknown quantity dependent on f. We construct two estimators and study their asymptotic properties.