LIMIT THEOREMS FOR POWER VARIATIONS OF PURE-JUMP PROCESSES WITH APPLICATION TO ACTIVITY ESTIMATION

• 成果类型: Article
• 署名作者: Todorov, Viktor; Tauchen, George
• 署名单位: Northwestern University; Duke University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/10-AAP700
• 发表日期: 2011
• 页码: 546-588
• 关键词: stochastic volatility

摘要

This paper derives the asymptotic behavior of realized power variation of pure-jump Ito semimartingales as the sampling frequency within a fixed interval increases to infinity. We prove convergence in probability and an associated central limit theorem for the realized power variation as a function of its power. We apply the limit theorems to propose an efficient adaptive estimator for the activity of discretely-sampled Ito semimartingale over a fixed interval.