Outlyingness Weighted Quadratic Covariation

Abstract:     
Quadratic Covariation (QCov) is a popular descriptive measure for the volatility of a multivariate price process. It is consistently estimated by the sum of outer products of high-frequency returns. This paper introduces the univariate and multivariate versions of the Realized Outlyingness Weighted Quadratic Covariation (ROWQCov) as an estimator for the QCov of the continuous component of the price diffusion. The new estimator equals a weighted sum of outer products of high-frequency returns and downweights returns that, because of jumps or other reasons, are outliers under the Brownian SemiMartingale (BSM) model. Under this model, the ROWQCov is a more efficient estimator for the Integrated Covariance (ICov) than the Realized BiPower Covariation (RBPCov), which is very popular in the univariate case. The ROWQCov is consistent for the ICov under the BSM with finite activity jumps model and, unlike the RBPCov, it is robust to jumps affecting contiguous returns, affine equivariant and yields positive semidefinite matrices. We illustrate this method on 15-minute return series of the EUR/USD and GBP/USD exchange rates.

Keywords: Continuous-time methods, high-frequency data, quadratic covariation, realized covolatility, semi-martingales

JEL Classifications: C14, C32

Working Paper Series