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Bootstrapping Realized Volatility

Bootstrapping Realized Volatility 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Econometrica Wiley

Bootstrapping Realized Volatility

Econometrica , Volume 77 (1) – Jan 1, 2009

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References (56)

Publisher
Wiley
Copyright
Copyright © 2009 Wiley Subscription Services, Inc., A Wiley Company
ISSN
0012-9682
eISSN
1468-0262
DOI
10.3982/ECTA5971
Publisher site
See Article on Publisher Site

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.

Journal

EconometricaWiley

Published: Jan 1, 2009

Keywords: ; ; ;

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