Abstract: This paper develops two modified CUSUM and QS tests to examine structural changes in volatility based on least absolute deviation (LAD) regression and consistent estimation of the long-run variance (LRV). We establish fairly mild conditions under which the new tests have standard null distributions and are consistent against any fixed alternatives that deviate from the null, including smooth changes, single or multiple breakpoints in volatility. In addition, the tests also have asymptotic unit powers against two classes of local alternatives approaching the null at different rates. Simulations are conducted to show better finite sample performance of the new tests relative to other popular tests especially in the presence of heavy-tailed innovations. Finally, two empirical applications to detection of structural changes in volatilities of U.S. dollar/Russian Ruble exchange rate and S&P 500 index highlight the usefulness of our tests in real datasets.

Key words and phrases: CUSUM test, heavy-tailed innovation, least absolute deviation, nonparametric estimation, QS test, structural change in volatility.