Unit root tests in the presence of an innovation variance break that has power against the mean break stationary alternative

We show that Perron’s [Perron, P., 1990. Testing for a unit root in a time series with a changing mean. Journal of Business and Economic Statistics 8, 153–162] unit root test can be oversized when there is a break in the innovation variance. We propose a modified Perron test that maintains its size, and has power against the mean-break stationary alternative.