NONPARAMETRIC CHANGE-POINT ANALYSIS OF VOLATILITY

• 成果类型: Article
• 署名作者: Bibinger, Markus; Jirak, Moritz; Vetter, Mathias
• 署名单位: Braunschweig University of Technology; University of Kiel
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/16-AOS1499
• 发表日期: 2017
• 页码: 1542-1578
• 关键词: inference; regression; models; CONVERGENCE; functionals

摘要

In this work, we develop change-point methods for statistics of highfrequency data. The main interest is in the volatility of an Ito semimartingale, the latter being discretely observed over a fixed time horizon. We construct a minimax-optimal test to discriminate continuous paths from paths with volatility jumps, and it is shown that the test can be embedded into a more general theory to infer the smoothness of volatilities. In a high-frequency setting, we prove weak convergence of the test statistic under the hypothesis to an extreme value distribution. Moreover, we develop methods to infer changes in the Hurst parameters of fractional volatility processes. A simulation study is conducted to demonstrate the performance of our methods in finite-sample applications.