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Bootstrapping Realized Volatility

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Author Info
Sílvia Gonçalves
Nour Meddahi

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Abstract

We propose bootstrap methods for a general class of nonlinear transformations of realized volatility which includes the raw version of realized volatility and its logarithmic transformation as special cases. We consider the independent and identically distributed (i.i.d.) bootstrap and the wild bootstrap (WB), and prove their first-order asymptotic validity under general assumptions on the log-price process that allow for drift and leverage effects. We derive Edgeworth expansions in a simpler model that rules out these effects. The i.i.d. bootstrap provides a second-order asymptotic refinement when volatility is constant, but not otherwise. The WB yields a second-order asymptotic refinement under stochastic volatility provided we choose the external random variable used to construct the WB data appropriately. None of these methods provides third-order asymptotic refinements. Both methods improve upon the first-order asymptotic theory in finite samples. Copyright 2009 The Econometric Society.

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File URL: http://hdl.handle.net/10.3982/ECTA5971
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Publisher Info
Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 77 (2009)
Issue (Month): 1 (01)
Pages: 283-306
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Handle: RePEc:ecm:emetrp:v:77:y:2009:i:1:p:283-306

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  1. repec:mop:credwp:09.05.84 is not listed on IDEAS
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  2. Ole E. Barndorff-Nielsen & Neil Shephard, 2005. "Variation, jumps, market frictions and high frequency data in financial econometrics," OFRC Working Papers Series 2005fe08, Oxford Financial Research Centre. [Downloadable!]
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  3. Neil Shephard & Ole E. Barndorff-Nielsen & Asger Lunde, 2006. "Subsampling realised kernels," Economics Series Working Papers 278, University of Oxford, Department of Economics. [Downloadable!]
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  4. Ole E Barndorff-Nielsen & Peter Hansen & Asger Lunde & Neil Shephard, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," OFRC Working Papers Series 2006fe05, Oxford Financial Research Centre. [Downloadable!]
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  5. Julien Chevallier & Benoît Sévi, 2009. "On the realized volatility of the ECX CO2 emissions 2008 futures contract: distribution, dynamics and forecasting," Working Papers halshs-00387286_v1, HAL. [Downloadable!]
  6. Jean Jacod & Yingying Li & Per A. Mykland & Mark Podolskij & Mathias Vetter, 2007. "Microstructure Noise in the Continuous Case: The Pre-Averaging Approach - JLMPV-9," CREATES Research Papers 2007-43, School of Economics and Management, University of Aarhus. [Downloadable!]
  7. Ole E. Barndorff-Nielsen & Sven Erik Graversen & Jean Jacod & Neil Shephard, 2005. "Limit theorems for bipower variation in financial econometrics," OFRC Working Papers Series 2005fe09, Oxford Financial Research Centre. [Downloadable!]
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  8. Andrew J. Patton & Kevin Sheppard, 2008. "Evaluating Volatility and Correlation Forecasts," OFRC Working Papers Series 2008fe22, Oxford Financial Research Centre. [Downloadable!]
  9. 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. [Downloadable!] (restricted)
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