Flat-Top Realized Kernel Estimation of Quadratic Covariation With Nonsynchronous and Noisy Asset Prices

This article develops a general multivariate additive noise model for synchronized asset prices and provides a multivariate extension of the generalized flat-top realized kernel estimators, analyzed earlier by Varneskov (2014), to estimate its quadratic covariation. The additive noise model allows for α-mixing dependent exogenous noise, random sampling, and an endogenous noise component that encompasses synchronization errors, lead-lag relations, and diurnal heteroscedasticity. The various components may exhibit polynomially decaying autocovariances. In this setting, the class of estimators considered is consistent, asymptotically unbiased, and mixed Gaussian at the optimal rate of convergence, n^1/4. A simple finite sample correction based on projections of symmetric matrices ensures positive definiteness without altering the asymptotic properties of the estimators. It, thereby, guarantees the existence of nonlinear transformations of the estimated covariance matrix such as correlations and realized betas, which inherit the asymptotic properties from the flat-top realized kernel estimators. An empirically motivated simulation study assesses the choice of sampling scheme and projection rule, and it shows that flat-top realized kernels have a desirable combination of robustness and efficiency relative to competing estimators. Last, an empirical analysis of signal detection and out-of-sample predictions for a portfolio of six stocks of varying size and liquidity illustrates the use and properties of the new estimators.