Nonparametric change-point analysis of volatility
Markus Bibinger, Moritz Jirak, Mathias Vetter
The Annals of Statistics · 2017 · Volume 45 · Issue 4
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.
Keywords
62G10, 62M10, high-frequency data, minimax-optimal test, nonparametric change-point test, stochastic volatility, volatility jumps
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