Covariance Estimation and Dynamic Asset-Allocation under Microstructure Effects via Fourier Methodology

Abstract

We analyze the properties of different estimators of multivariate volatilities in the presence of microstructure noise, with particular focus on the Fourier estimator. This estimator is consistent in the case of asynchronous data and is robust to microstructure effects; further, we prove the positive semi-definiteness of the estimated covariance matrix. The in-sample and forecasting properties of the Fourier method are analyzed through Monte Carlo simulations. We study the economic benefit of applying the Fourier covariance estimation methodology over other estimators in the presence of market microstructure noise from the perspective of an asset-allocation decision problem. We find that using Fourier methodology yields statistically significant economic gains under strong microstructure effects.ReferencesKeywordsMean Square ErrorCovariance EstimationForecast HorizonMicrostructure NoiseQuadratic CovariationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.