Cross-Sectional Noise Reduction and More Efficient Estimation of Integrated Variance

Abstract

In this paper we propose a straightforward approach to obtain a more efficient estimate of the integrated variance of an asset through a cross-sectional combination with a futures contract written on it. Our method constructs a variance-preserving series with reduced noise size as a linear combination of the underlying asset and the futures and base measurement of the integrated variance on this new series. We first illustrate how a theoretically but infeasible optimal series can be obtained and then suggest a feasible procedure to attain noise reduction. In a simulation study we verify how prevalent estimators of integrated variance applied to such noise-reduced series outperform estimators applied directly to the asset price. Finally, we apply the method to an empirical data set and, through the stabilized signature plot, we show how the noise reduced series provides consistent integrated variance estimates using naive realized measures at very high frequencies.