Detecting structural changes under nonstationary volatility

•The U-statistic proposed by Juhl and Xiao (2013) can be used to test against structural changes under nonstationary volatility.•The test allows for conditional heteroskedasticity and time-varying unconditional variance, and can detect any smooth or abrupt structural changes.•We advocate using a bootstrap method to improve the size performance in finite samples.

This paper shows that the U-statistic for moment condition stability proposed by Juhl and Xiao (2013) can be used to test against structural changes in regression coefficients under nonstationary volatility. We investigate the power property under the alternative, and prove that the test is consistent against single break, multiple breaks and smooth structural changes. Finally, we advocate using a bootstrap method to improve its size performance in finite samples.