LIMIT THEOREMS FOR THE EMPIRICAL DISTRIBUTION FUNCTION OF SCALED INCREMENTS OF ITO SEMIMARTINGALES AT HIGH FREQUENCIES

• 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: 10.1214/13-AAP965
• 发表日期: 2014
• 页码: 1850-1888
• 关键词: models; inference; motion

摘要

We derive limit theorems for. the empirical distribution function of de-volatilized increments of an Ito semimartingale observed at high frequencies. These devolatilized increments are formed by suitably rescaling and truncating the raw increments to remove the effects of stochastic volatility and large jumps. We derive the limit of the empirical c.d.f. of the adjusted increments for any Ito semimartingale whose dominant component at high frequencies has activity index of 1 < beta <= 2, where beta = 2 corresponds to diffusion. We further derive an associated CLT in the jump-diffusion case. We use the developed limit theory to construct a feasible and pivotal test for the class of Ito semimartingales with nonvanishing diffusion coefficient against Ito semimartingales with no diffusion component.