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Moving average-based estimators of integrated variance. (English) Zbl 1148.62088
Summary: We examine moving average (MA) filters for estimating the integrated variance (IV) of a financial asset price in a framework where high-frequency price data are contaminated with market microstructure noise. We show that the sum of squared MA residuals must be scaled to enable a suitable estimator of the IV. 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 time-varying volatility, the MA model is misspecified. This motivates an extensive simulation study of the merits of the MA-based estimator under misspecification. Specifically, we consider nonconstant 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.

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
91B28 Finance etc. (MSC2000)
65C60 Computational problems in statistics (MSC2010)
62M20 Inference from stochastic processes and prediction
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