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Edgeworth Corrections for Realized Volatility

Author

Listed:
  • Silvia Goncalves
  • Nour Meddahi

Abstract

The quality of the asymptotic normality of realized volatility can be poor if sampling does not occur at very high frequencies. In this article we consider an alternative approximation to the finite sample distribution of realized volatility based on Edgeworth expansions. In particular, we show how confidence intervals for integrated volatility can be constructed using these Edgeworth expansions. The Monte Carlo study we conduct shows that the intervals based on the Edgeworth corrections have improved properties relatively to the conventional intervals based on the normal approximation. Contrary to the bootstrap, the Edgeworth approach is an analytical approach that is easily implemented, without requiring any resampling of one's data. A comparison between the bootstrap and the Edgeworth expansion shows that the bootstrap outperforms the Edgeworth corrected intervals. Thus, if we are willing to incur in the additional computational cost involved in computing bootstrap intervals, these are preferred over the Edgeworth intervals. Nevertheless, if we are not willing to incur in this additional cost, our results suggest that Edgeworth corrected intervals should replace the conventional intervals based on the first order normal approximation.

Suggested Citation

  • Silvia Goncalves & Nour Meddahi, 2008. "Edgeworth Corrections for Realized Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 139-162.
  • Handle: RePEc:taf:emetrv:v:27:y:2008:i:1-3:p:139-162
    DOI: 10.1080/07474930701870420
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    References listed on IDEAS

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    1. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    2. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
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    Cited by:

    1. Dovonon, Prosper & Gonçalves, Sílvia & Meddahi, Nour, 2013. "Bootstrapping realized multivariate volatility measures," Journal of Econometrics, Elsevier, vol. 172(1), pages 49-65.
    2. Zhang, Lan & Mykland, Per A. & Aït-Sahalia, Yacine, 2011. "Edgeworth expansions for realized volatility and related estimators," Journal of Econometrics, Elsevier, vol. 160(1), pages 190-203, January.
    3. Ulrich Hounyo & Bezirgen Veliyev, 2016. "Validity of Edgeworth expansions for realized volatility estimators," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 1-32, February.

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