Two-scale realized kernels: a univariate case

ikeda. s, shin;

A bias-corrected nonparametric estimator of daily quadratic variations
is proposed. The estimator is a convex combination of two realized
kernels with different bandwidths. It converges to the true quadratic
variation at the best parametric rate in the presence of a serially
dependent noise. Its asymptotic distribution is correctly centered, thus facilitating the feasible inference of an estimate using the asymptotic approximation. By appropriately designing the weight function, the proposed estimator can achieve the parametric efficiency bound of the asymptotic variance. I also propose a finite sample correction to ensure that the transformed version is nonnegative. Simulation results show that the proposed estimator has good finite sample properties compared with several noise-robust estimators including the original realized kernel estimator.