High-dimensional Realized Covariance Estimation : a Parametric Approach

The estimation of the covariances of high-frequency asset prices is problematic because of asynchronous trading and market microstructure noise. In the last years, both parametric and non-parametric methods have been proposed in order to handle these effects. Little attention has instead been devoted to the curse of dimensionality problem, which makes the use of standard methodologies prohibitive when the cross-section dimension increases. In this paper, we introduce a parametric factor structure which allows for dimensionality reduction and simplifies considerably the inference problem. We test our method in an empirical setting that emphasizes the effect of the curse of dimensionality. Compared to standard parametric approaches, our factor specification is computationally simpler and provides statistically indistinguishable performances in standard risk management applications