Change-point inference on volatility in noisy It\^o semimartingales

TL;DR

This paper develops a statistical test for detecting structural breaks in the volatility of noisy Itô semimartingales, using spectral estimates and extreme value theory, with proven consistency and good finite-sample performance.

Contribution

It introduces a novel consistent testing procedure for volatility change-points in noisy semimartingales based on spectral methods and asymptotic analysis.

Findings

The test is consistent under the null hypothesis.

The estimator accurately detects change points.

Simulation shows improved performance over skip-sampling methods.

Abstract

This work is concerned with tests on structural breaks in the spot volatility process of a general It\^o semimartingale based on discrete observations contaminated with i.i.d. microstructure noise. We construct a consistent test building up on infill asymptotic results for certain functionals of spectral spot volatility estimates. A weak limit theorem is established under the null hypothesis relying on extreme value theory. We prove consistency of the test and of an associated estimator for the change point. A simulation study illustrates the finite-sample performance of the method and efficiency gains compared to a skip-sampling approach.