Powerful tests for structural changes in volatility

Detecting structural changes in volatility is important for understanding volatility dynamics and stylized facts observed for financial returns such as volatility persistence. We propose modified CUSUM and LM tests that are built on a robust estimator of the long-run variance of squared series. We establish conditions under which the new tests have standard null distributions and diverge faster than standard tests under the alternative. The theory allows smooth and abrupt structural changes that can be small. The smoothing parameter is automatically selected such that the proposed test has good finite-sample size and meanwhile achieves decent power gain.