Abstract: This work develops change-point methods for statistics of high-frequency data. The main interest is the volatility of an Itô semi-martingale, which is discretely observed over a fixed time horizon. We construct a minimax-optimal test to discriminate different smoothness classes of the underlying stochastic volatility process. In a high-frequency framework we prove weak convergence of the test statistic under the hypothesis to an extreme value distribution. As a key example, under extremely mild smoothness assumptions on the stochastic volatility we thereby derive a consistent test for volatility jumps. A simulation study demonstrates the practical value in finite-sample applications.
REF construct a nonparametric minimax-optimal test to discriminate continuous paths with volatility jumps and prove weak convergence of the test statistic to an extreme value distribution.
Nonparametric change-point analysis of volatility
arXiv: Statistics Theory
Mathematics