Sign-based tests for structural changes in multivariate volatility

Abstract

This paper proposes sign-based CUSUM and QS tests for structural changes in multivariate volatility using least absolute deviation (LAD) regression. These tests offer the advantage of relaxing moment conditions and providing greater robustness against various heavy-tailed innovations. To address potential power losses in the two basic statistics due to inaccurate estimation of the long-run variance (LRV) under alternatives, the paper then proposes two modified statistics that utilize LAD nonparametric methods for consistent estimation of the LRV under both the null and alternative hypotheses. The study establishes relatively mild conditions under which these tests have standard null distributions and are powerful against various fixed alternatives, including smooth changes and single or multiple breakpoints in multivariate volatility. Additionally, the paper examines the asymptotic properties of the modified statistics under two different types of local alternatives. Monte Carlo simulations demonstrate that the proposed tests outperform other widely used tests in finite samples when dealing with heavy-tailed data. Two empirical applications to financial datasets further confirm the effectiveness of the new testing methods.