Realized range-based estimation of integrated variance

Realized range-based estimation of integrated variance We provide a set of probabilistic laws for estimating the quadratic variation of continuous semimartingales with the realized range-based variance—a statistic that replaces every squared return of the realized variance with a normalized squared range. If the entire sample path of the process is available, and under a set of weak conditions, our statistic is consistent and has a mixed Gaussian limit, whose precision is five times greater than that of the realized variance. In practice, of course, inference is drawn from discrete data and true ranges are unobserved, leading to downward bias. We solve this problem to get a consistent, mixed normal estimator, irrespective of non-trading effects. This estimator has varying degrees of efficiency over realized variance, depending on how many observations that are used to construct the high–low. The methodology is applied to TAQ data and compared with realized variance. Our findings suggest that the empirical path of quadratic variation is also estimated better with the realized range-based variance. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Econometrics Elsevier

Realized range-based estimation of integrated variance

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Publisher
Elsevier
Copyright
Copyright © 2006 Elsevier B.V.
ISSN
0304-4076
eISSN
1872-6895
D.O.I.
10.1016/j.jeconom.2006.06.012
Publisher site
See Article on Publisher Site

Abstract

We provide a set of probabilistic laws for estimating the quadratic variation of continuous semimartingales with the realized range-based variance—a statistic that replaces every squared return of the realized variance with a normalized squared range. If the entire sample path of the process is available, and under a set of weak conditions, our statistic is consistent and has a mixed Gaussian limit, whose precision is five times greater than that of the realized variance. In practice, of course, inference is drawn from discrete data and true ranges are unobserved, leading to downward bias. We solve this problem to get a consistent, mixed normal estimator, irrespective of non-trading effects. This estimator has varying degrees of efficiency over realized variance, depending on how many observations that are used to construct the high–low. The methodology is applied to TAQ data and compared with realized variance. Our findings suggest that the empirical path of quadratic variation is also estimated better with the realized range-based variance.

Journal

Journal of EconometricsElsevier

Published: Dec 1, 2007

References

  • Separating microstructure noise from volatility
    Bandi, F.M.; Russell, J.R.
  • Econometric analysis of realized volatility and its use in estimating stochastic volatility models
    Barndorff-Nielsen, O.E.; Shephard, N.
  • Power and bipower variation with stochastic volatility and jumps
    Barndorff-Nielsen, O.E.; Shephard, N.
  • Measuring volatility with the realized range
    Dijk, D.J.C.V.; Martens, M.
  • A realized variance for the whole day based on intermittent high-frequency data
    Hansen, P.R.; Lunde, A.
  • Properties of bias-corrected realized variance under alternative sampling schemes
    Oomen, R.C.A.

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