Bootstrapping Volatility Functionals:A Local And Non-parametric Perspective

Volatility functionals are widely used in financial econometrics.In the literature,they are estimated by the realized volatility functionals with high-frequency data and related central limit theorems are established.In this paper,we introduce a nonparamet-ric bootstrap method which resamples(with replacement)the high-frequency returns in local windows shrinking to O.While the block bootstrap in time series(cf,Hall et al[1])is aimed at reducing the correlation,the local bootstrap is to eliminate the heterogene-ity.We prove that the bootstrap distribution of the realized volatility functional is first order accurate.We also present the Edgeworth expansions of the studentized realized volatility functionals and bootstrapped volatility functionals in absence of leverage ef-fect.In particular,when the volatility functional is the integrated volatility,the local nonparametric bootstrap distribution of the studentized realized variance is of second order accuracy under some mild conditions.Extensive simulation studies verify the theory and real data sets are analyzed.