Bootstrapping volatility functionals: a local and nonparametric perspective
提出一种局部非参数Bootstrap方法，通过在高频收益率局部窗口内重抽样来消除波动率异质性，证明学生化已实现波动率泛函的Bootstrap分布具有一阶和二阶准确性，并通过模拟验证。
Volatility functionals are widely used in financial econometrics. In the literature, they are estimated with realized volatility functionals using high-frequency data. In this paper we introduce a nonparametric local bootstrap method that resamples the high-frequency returns with replacement in local windows shrinking to zero. While the block bootstrap in time series (Hall et al., 1995) aims to reduce correlation, the local bootstrap is intended to eliminate the heterogeneity of volatility. We prove that the local bootstrap distribution of the studentized realized volatility functional is first-order accurate. We present Edgeworth expansions of the studentized realized variance with and without local bootstrapping in the absence of the leverage effect and jumps. The expansions show that the local bootstrap distribution of the studentized realized variance is second-order accurate. Extensive simulation studies verify the theory.