Open Access
August 2017 Nonparametric change-point analysis of volatility
Markus Bibinger, Moritz Jirak, Mathias Vetter
Ann. Statist. 45(4): 1542-1578 (August 2017). DOI: 10.1214/16-AOS1499


In this work, we develop change-point methods for statistics of high-frequency data. The main interest is in the volatility of an Itô 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.


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Markus Bibinger. Moritz Jirak. Mathias Vetter. "Nonparametric change-point analysis of volatility." Ann. Statist. 45 (4) 1542 - 1578, August 2017.


Received: 1 February 2016; Revised: 1 June 2016; Published: August 2017
First available in Project Euclid: 28 June 2017

zbMATH: 06773283
MathSciNet: MR3670188
Digital Object Identifier: 10.1214/16-AOS1499

Primary: 62M10
Secondary: 62G10

Keywords: high-frequency data , minimax-optimal test , nonparametric change-point test , stochastic volatility , volatility jumps

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.45 • No. 4 • August 2017
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