Bootstrapping Realized Multivariate Volatility Measures

34 Pages Posted: 5 Nov 2009

See all articles by Prosper Dovonon

Prosper Dovonon

Barclays Wealth

Sílvia Gonçalves

University of Montreal - Department of Economics

Nour Meddahi

University of Toulouse 1 - Toulouse School of Economics (TSE)

Date Written: February 24, 2009

Abstract

We study bootstrap methods for statistics that are a function of multivariate high frequency returns such as realized regression coefficients and realized covariances and correlations. For these measures of covariation, the Monte Carlo simulation results of Barndorff-Nielsen and Shephard (2004) show that finite sample distortions associated with their feasible asymptotic theory approach may arise if sampling is not too frequent. This motivates our use of the bootstrap as an alternative tool of inference for covariation measures.

We consider an i.i.d. bootstrap applied to the vector of returns. We show that the finite sample performance of the bootstrap is superior to the existing first-order asymptotic theory. Nevertheless, and contrary to the existing results in the bootstrap literature for regression models subject to heteroskedasticity in the error term, the Edgeworth expansion for the i.i.d. bootstrap that we develop here shows that this method is not second order accurate. We argue that this is due to the fact that the conditional mean parameters of realized regression models are heterogeneous under stochastic volatility.

Keywords: Realized regression, realized beta, realized correlation, bootstrap, Edgeworth expansions

Suggested Citation

Dovonon, Prosper and Goncalves, Silvia and Meddahi, Nour, Bootstrapping Realized Multivariate Volatility Measures (February 24, 2009). Available at SSRN: https://ssrn.com/abstract=1500028 or http://dx.doi.org/10.2139/ssrn.1500028

Prosper Dovonon (Contact Author)

Barclays Wealth ( email )

1, Churchill Place
London, E14 5HP
United Kingdom

Silvia Goncalves

University of Montreal - Department of Economics ( email )

C.P. 6128, succursale Centre-Ville
Montreal, Quebec H3C 3J7
Canada

Nour Meddahi

University of Toulouse 1 - Toulouse School of Economics (TSE) ( email )

Place Anatole-France
Toulouse Cedex, F-31042
France

HOME PAGE: http://gremaq.univ-tlse1.fr/perso/meddahi/

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