Edgeworth Corrections for Realized Volatility
AbstractThe 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.
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Bibliographic InfoArticle provided by Taylor & Francis Journals in its journal Econometric Reviews.
Volume (Year): 27 (2008)
Issue (Month): 1-3 ()
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- 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.
- Lan Zhang & Per A. Mykland & Yacine Ait-Sahalia, 2005. "Edgeworth Expansions for Realized Volatility and Related Estimators," NBER Technical Working Papers 0319, National Bureau of Economic Research, Inc.
- Dovonon, Prosper & Gonçalves, Sílvia & Meddahi, Nour, 2013.
"Bootstrapping realized multivariate volatility measures,"
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Elsevier, vol. 172(1), pages 49-65.
- Dovonon, Prosper & Goncalves, Silvia & Meddahi, Nour, 2010. "Bootstrapping realized multivariate volatility measures," MPRA Paper 40123, University Library of Munich, Germany.
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