LIMIT THEOREMS FOR MOVING AVERAGES OF DISCRETIZED PROCESSES PLUS NOISE

• 成果类型: Article
• 署名作者: Jacod, Jean; Podolskij, Mark; Vetter, Mathias
• 署名单位: Universite Paris Cite; Sorbonne Universite; Swiss Federal Institutes of Technology Domain; ETH Zurich; Ruhr University Bochum
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS756
• 发表日期: 2010
• 页码: 1478-1545
• 关键词: MICROSTRUCTURE NOISE; volatility; functionals

摘要

This paper presents some limit theorems for certain functionals of moving averages of semimartingales plus noise which are observed at high frequency. Our method generalizes the pre-averaging approach (see [Bernoulli 15 (2009) 634-658, Stochastic Process. Appl. 119 (2009) 2249-2276]) and provides consistent estimates for various characteristics of general semimartingales. Furthermore, we prove the associated multidimensional (stable) central limit theorems. As expected, we find central limit theorems with a convergence rate n(-1/4), if it is the number of observations.