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Abstract |
Volatility functionals are widely used in financial econometrics. In existing literatures, they are estimated by the realized volatility functionals with high-frequency data and related central limit theorems are established. However, the presence of the microstructure noise hinders the accuracy of the normal approximation and hence in many situations this is remedied by sparsely sampling the high-frequency data. This makes the normal approximation less accurate because of the small effective sample size. In this paper, we introduce a non-parametric bootstrap method which locally resamples (with replacement) the high-frequency returns in a local window shrinking to 0. We prove that the bootstrap distribution of the realized volatility functional is first order accurate, and could be second order accurate if one assumes absence of leverage effect. Extensive simulation studies verify the performance of the theory and real data sets are analyzed. |
