Bootstrapping volatility functionals: a local and nonparametric perspective

• 成果类型: Article
• 署名作者: Kong, Xin-Bing; Xu, Shao-Jun; Zhou, Wang
• 署名单位: Nanjing Audit University; Shanghai University of Finance & Economics; National University of Singapore
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asy002
• 发表日期: 2018
• 页码: 463469
• 关键词: Realized volatility; microstructure noise; models; jumps

摘要

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.