The Dickey-Fuller unit root test is known to suffer severe oversizing in the presence of innovation variance breaks. In this paper, forward and reverse Dickey-Fuller regressions are proposed as a means of correcting this size distortion. The results of Monte Carlo experimentation show such an approach to result in both satisfactory size properties and increased power relative to previously suggested solutions.
Steven Cook. "Unit root testing in the presence of innovation variance breaks: a simple solution with increased power." J. Appl. Math. 2 (5) 233 - 240, 22 September 2002. https://doi.org/10.1155/S1110757X02107029