Generalized Flat-Top Realized Kernel Estimation of Ex-Post Variation of Asset Prices Contaminated by Noise

This paper introduces a new class of generalized flat-top realized kernels for estimation of quadratic variation in the presence of market microstructure noise that is allowed to exhibit a non-trivial dependence structure and to be correlated with the efficient price process. The estimators in this class are shown to be consistent, asymptotically unbiased, and mixed gaussian with an optimal n^(1/4)-convergence rate. In addition, an efficient and asymptotically normal estimator of the long run variance of the market microstructure noise is provided along with novel and consistent estimators of the asymptotic variance of the flat-top realized kernels and of the integrated quarticity, respectively, creating a powerful, unified framework for analyzing quadratic variation. A finite sample correction ensures non-negativity of the at-top realized kernels without a effecting asymptotic properties. Lastly, in an extensive simulation study, important practical issues such as the choice of kernel function and tuning parameters are addressed, the adequacy of the asymptotic distribution in finite samples is assessed, and it is shown that estimators in this class exhibit a superior bias and root mean squared error tradeo relative to competing estimators. The impact of using various realized estimators is illustrated in a small empirical application to noisy high frequency stock market data.