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We study bootstrap methods for statistics that are a function of multivariate high frequencyreturns such as realized regression coefficients and realized covariances and correlations. For thesemeasures of covariation, the Monte Carlo simulation results of Barndorff-Nielsen and Shephard(2004) show that finite sample distortions associated with their feasible asymptotic theory approachmay arise if sampling is not too frequent. This motivates our use of the bootstrap as an alternativetool of inference for covariation measures.We consider an i.i.d. bootstrap applied to the vector of returns. We show that the finite sampleperformance 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 toheteroskedasticity in the error term, the Edgeworth expansion for the i.i.d. bootstrap that wedevelop here shows that this method is not second order accurate. We argue that this is due to thefact that the conditional mean parameters of realized regression models are heterogeneous understochastic volatility.

Bootstrapping Realized Multivariate Volatility Measures