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EFFICIENT ESTIMATION OF INTEGRATED VOLATILITY AND RELATED PROCESSES

Éric Renault · Cisil Sarisoy · Bas J. M. Werker

30 citations0/0 files storedEconometric Theory

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Financial Risk and Volatility Modeling Stochastic processes and financial applications Statistical Methods and Inference

Abstract

We derive nonparametric efficiency bounds for regular estimators of integrated smooth transformations of instantaneous variances, in particular, integrated power variance. We find that realized variance attains the efficiency bound for integrated variance under both regular and irregular sampling schemes. For estimating higher powers such as integrated quarticity, the block-based procedures of Mykland and Zhang (2009) can get arbitrarily close to the nonparametric bounds, when observation times are equidistant. Moreover, the estimator in Jacod and Rosenbaum (2013), whose efficiency was documented for the submodel assuming constant volatility, is efficient also for nonconstant volatility paths. When the observation times are possibly random but predictable, we provide an estimator, similar to that of Kristensen (2010), which can get arbitrarily close to the nonparametric bound. Finally, parametric information about the functional form of volatility leads to a lower efficiency bound, unless the volatility process is piecewise constant.

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References

1999Continuous Martingales and Brownian Motion 2003Modeling and Forecasting Realized Volatility 1998Answering the Skeptics: Yes, Standard Volatility Models do Provide Accurate Forecasts 1980On estimating the expected return on the market 2003Limit Theorems for Stochastic Processes 2002Econometric Analysis of Realized Volatility and its Use in Estimating Stochastic Volatility Models 2001The Distribution of Realized Exchange Rate Volatility 2004Power and Bipower Variation with Stochastic Volatility and Jumps

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2020Estimation for high-frequency data under parametric market microstructure noise 2015Functional stable limit theorems for quasi-efficient spectral covolatility estimators 2019Testing if the market microstructure noise is fully explained by the informational content of some variables from the limit order book

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