A TEST FOR THE RANK OF THE VOLATILITY PROCESS: THE RANDOM PERTURBATION APPROACH

• 成果类型: Article
• 署名作者: Jacod, Jean; Podolskij, Mark
• 署名单位: Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ruprecht Karls University Heidelberg
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/13-AOS1153
• 发表日期: 2013
• 页码: 2391-2427
• 关键词: asymptotic properties; SEMIMARTINGALES

摘要

In this paper, we present a test for the maximal rank of the matrix-valued volatility process in the continuous Ito semimartingale framework. Our idea is based upon a random perturbation of the original high frequency observations of an Ito semimartingale, which opens the way for rank testing. We develop the complete limit theory for the test statistic and apply it to various null and alternative hypotheses. Finally, we demonstrate a homoscedasticity test for the rank process.