EFFICIENT ESTIMATION OF INTEGRATED VOLATILITY FUNCTIONALS VIA MULTISCALE JACKKNIFE

• 成果类型: Article
• 署名作者: Li, Jia; Liu, Yunxiao; Xiu, Dacheng
• 署名单位: Duke University; University of North Carolina; University of North Carolina Chapel Hill; University of Chicago
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1684
• 发表日期: 2019
• 页码: 156-176
• 关键词: econometric-analysis; equity prices; covariation; regression; inference; moments

摘要

We propose semiparametrically efficient estimators for general integrated volatility functionals of multivariate semimartingale processes. A plug-in method that uses nonparametric estimates of spot volatilities is known to induce high-order biases that need to be corrected to obey a central limit theorem. Such bias terms arise from boundary effects, the diffusive and jump movements of stochastic volatility and the sampling error from the nonparametric spot volatility estimation. We propose a novel jackknife method for bias correction. The jackknife estimator is simply formed as a linear combination of a few uncorrected estimators associated with different local window sizes used in the estimation of spot volatility. We show theoretically that our estimator is asymptotically mixed Gaussian, semiparametrically efficient, and more robust to the choice of local windows. To facilitate the practical use, we introduce a simulation-based estimator of the asymptotic variance, so that our inference is derivative-free, and hence is convenient to implement.