Nonparametric change-point analysis of volatility

TL;DR

This paper introduces nonparametric change-point detection methods for high-frequency financial data, focusing on volatility jumps, smoothness, and fractional processes, with proven theoretical properties and practical simulation results.

Contribution

It develops minimax-optimal tests for volatility jumps and smoothness, and methods to infer changes in the Hurst parameter, advancing high-frequency volatility analysis.

Findings

Weak convergence of test statistic to an extreme value distribution

Effective detection of volatility jumps in finite samples

Methods for inferring changes in fractional volatility processes

Abstract

This work develops change-point methods for statistics of high-frequency data. The main interest is in the volatility of an It\^{o} semi-martingale, the latter being discretely observed over a fixed time horizon. We construct a minimax-optimal test to discriminate continuous paths from paths comprising volatility jumps. This is embedded into a more general theory to infer the smoothness of volatilities. In a high-frequency framework 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 parameter of fractional volatility processes. A simulation study demonstrates the practical value in finite-sample applications.