LIMIT THEOREMS FOR NONDEGENERATE U-STATISTICS OF CONTINUOUS SEMIMARTINGALES

• 成果类型: Article
• 署名作者: Podolskij, Mark; Schmidt, Christian; Ziegel, Johanna F.
• 署名单位: Ruprecht Karls University Heidelberg; University of Bern
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/13-AAP983
• 发表日期: 2014
• 页码: 2491-2526
• 关键词: asymptotic properties; mean difference; dependent data; functionals; volatility; dimension; models

摘要

This paper presents the asymptotic theory for nondegenerate U-statistics of high frequency observations of continuous Ito semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem for the standardized version of the U-statistic. The limiting process in the central limit theorem turns out to be conditionally Gaussian with mean zero. Finally, we indicate potential statistical applications of our probabilistic results.