Moving Average-Based Estimators of Integrated Variance

Abstract

We examine moving average (MA) filters for estimating the integrated variance of a financial asset price in a framework where high frequency price data are contaminated with marketmicrostructure noise. We show that the sum of squared MA residuals needs to be scaled for it to be a suitable estimator of integrated variance. The scaled estimator is shown to be consistent, first-order efficient, and asymptotically Gaussian distributed about the integrated variance under restrictive assumptions. Under more plausible assumptions, such as timevarying volatility, the MA model is misspecified. This motivates an extensive simulation study of the merits of the MA-based estimator under mispecification. Specifically we consider: non-constant volatility combined with rounding errors and various forms of dependence between the noise and efficient returns. We benchmark the scaled MA-based estimator to subsample and realized kernel estimators and find that the MA-based estimator performs well despite the misspecification.