Efficient Estimation of Integrated Volatility and Related Processes

38 Pages Posted: 14 Jul 2013 Last revised: 21 Jan 2015

See all articles by Eric Renault

Eric Renault

University of North Carolina (UNC) at Chapel Hill - Department of Economics

Cisil Sarisoy

Board of Governors of the Federal Reserve System

Bas J. M. Werker

Tilburg University - Center for Economic Research (CentER)

Date Written: January 16, 2015

Abstract

We derive nonparametric bounds for inference about functionals of high-frequency volatility, in particular, integrated power variance. In the absence of microstructure noise, we find that standard Realized Variance attains the nonparametric efficiency bound, also in case of unequally spaced random observation times. For higher powers, e.g., integrated quarticity, the block-based procedures of Mykland and Zhang (2009) can get arbitrarily close to the nonparametric bounds in case of equally spaced observations. The estimator in Jacod and Rosenbaum (2013) is efficient, also at non-constant volatility, still for equally spaced data. For unequally spaced data, we provide an estimator, similar to that of Kristensen (2010), that can get arbitrarily close to the nonparametric bound. Finally, contrary to public opinion, we demonstrate that parametric information about the functional form of volatility generally leads to a decreased lower bound, unless the volatility process is piecewise constant.

Keywords: High-frequency data, Integrated power variance, Local Asymptotic Normality, Nonparametric efficiency bounds, Realized volatility, Volatility estimation

Suggested Citation

Renault, Eric and Sarisoy, Cisil and Werker, Bas J.M., Efficient Estimation of Integrated Volatility and Related Processes (January 16, 2015). Available at SSRN: https://ssrn.com/abstract=2293570 or http://dx.doi.org/10.2139/ssrn.2293570

Eric Renault

University of North Carolina (UNC) at Chapel Hill - Department of Economics ( email )

Chapel Hill, NC 27599
United States

Cisil Sarisoy

Board of Governors of the Federal Reserve System ( email )

20th Street and Constitution Avenue NW
Washington, DC 20551
United States

Bas J.M. Werker (Contact Author)

Tilburg University - Center for Economic Research (CentER) ( email )

Econometrics and Finance Group
5000 LE Tilburg
Netherlands

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