A bias-corrected estimator of the covariation matrix of multiple security prices when both microstructure effects and sampling durations are persistent and endogenous

I propose a bias-corrected non-parametric estimator of the covariation matrix of log security prices, designed as a convex combination of two realized kernels. The estimator is simple but possesses desirable statistical properties including consistency, asymptotic normality and the parametric rate of convergence in the presence of persistent, diurnally heteroskedastic and endogenous microstructure effects. It is robust to the asynchronous trading of multiple securities with persistent and endogenous refresh-time durations. I also prove the consistency of a subsampling-based estimator of the asymptotic covariance matrix of the proposed estimator. In simulations, the non-linear functions of the proposed estimator exhibit smaller bias than those based on a realized kernel, while only slightly increasing the variance. Thereby, the proposed estimator reduces the mean squared error.