Unit root tests with a break in innovation variance

It is shown that an abrupt change in the innovation variance of an integrated process can generate spurious rejections of the unit root null hypothesis in routine applications of Dickey–Fuller tests. We develop and investigate modified test statistics, based on unit root tests of Perron for a time series with a changing level, or changing intercept and slope, which are applicable when there is a change in innovation variance of an unknown magnitude at an unknown location.