## The Annals of Statistics

### Nonparametric change-point analysis of volatility

#### Abstract

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.

#### Article information

Source
Ann. Statist., Volume 45, Number 4 (2017), 1542-1578.

Dates
Revised: June 2016
First available in Project Euclid: 28 June 2017

https://projecteuclid.org/euclid.aos/1498636866

Digital Object Identifier
doi:10.1214/16-AOS1499

Mathematical Reviews number (MathSciNet)
MR3670188

Zentralblatt MATH identifier
06773283

Subjects
Secondary: 62G10: Hypothesis testing

#### Citation

Bibinger, Markus; Jirak, Moritz; Vetter, Mathias. Nonparametric change-point analysis of volatility. Ann. Statist. 45 (2017), no. 4, 1542--1578. doi:10.1214/16-AOS1499. https://projecteuclid.org/euclid.aos/1498636866

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#### Supplemental materials

• Complete proofs. We provide all remaining proofs for the results from Sections 3, 4 and 5.
• Application and simulations. We present complementary simulations for different sample sizes accompanied by a sensitivity analysis of the dependence on $k_{n}$ and a discussion of data applications.