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Estimating quadratic variation using realised volatility

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This paper looks at some recent work on estimating quadratic variation using realised volatility (RV) - that is sums of M squared returns. When the underlying process is a semimartingale we recall the fundamental result that RV is a consistent estimator of quadratic variation (QV). We express concern that without additonal assumptions it seems difficult to given any measure of uncertainty of the RV in this context. The position dramatically changes when we work with a rather general SV model - which is a special case of the semimartingale model. Then QV is integrated volatility and we can derive the asymptotic distribution of the RV and its rate of convergence. These results do not require us to specify a model for either the drift or volatility functions, although we have to impose some weak regularity assumptions. We illustrate the use of the limit theory on some exchange rate data. We show that even with the large values of M and RV is sometimes a quite noisy estimator of integrated volatility

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  • Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Estimating quadratic variation using realised volatility," Economics Papers 2001-W20, Economics Group, Nuffield College, University of Oxford, revised 01 Nov 2001.
  • Handle: RePEc:nuf:econwp:0120
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    1. Poterba, James M & Summers, Lawrence H, 1986. "The Persistence of Volatility and Stock Market Fluctuations," American Economic Review, American Economic Association, vol. 76(5), pages 1142-1151, December.
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    6. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280.
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    Cited by:

    1. Peter Reinhard Hansen & Asger Lunde & James M. Nason, 2003. "Choosing the Best Volatility Models: The Model Confidence Set Approach," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(s1), pages 839-861, December.
    2. Nour Meddahi, 2001. "A Theoretical Comparison Between Integrated andRealized Volatilities / A Theoretical Comparison Between Integrated and Realized Volatilities," CIRANO Working Papers 2001s-71, CIRANO.

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    Keywords

    Power variation; Quadratic variation; Realised volatility; Semimartingale; Volatility.;

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