ESTIMATING THE DEGREE OF ACTIVITY OF JUMPS IN HIGH FREQUENCY DATA

• 成果类型: Article
• 署名作者: Ait-Sahalia, Yacine; Jacod, Jean
• 署名单位: Princeton University; National Bureau of Economic Research; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS640
• 发表日期: 2009
• 页码: 2202-2244
• 关键词: Levy processes; tail

摘要

We define a generalized index of jump activity, propose estimators of that index for a discretely sampled process and derive the estimators' properties. These estimators are applicable despite the presence of Brownian volatility in the process, which makes it more challenging to infer the characteristics of the small, infinite activity jumps. When the method is applied to high frequency stock returns, we find evidence of infinitely active jumps in the data and estimate their index of activity.