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2009) Bootstraping realized volatility

By Gonçalves and Nour Meddahi

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 thirdorder asymptotic refinements. Both methods improve upon the first-order asymptotic theory in finite samples

Topics: Realized volatility, i.i.d. bootstrap, wild bootstrap, Edgeworth expansions
Year: 2012
OAI identifier: oai:CiteSeerX.psu:10.1.1.232.8832
Provided by: CiteSeerX
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