This paper proves the weak convergence of the residual empirical process in an explosive autoregression model to the Brownian bridge. As an application the Kolmogorov-Smirnov goodness-of-fit test for testing that the errors have a specified distribution is shown to be asymptotically distribution-free.
"Weak Convergence of the Residual Empirical Process in Explosive Autoregression." Ann. Statist. 17 (4) 1784 - 1794, December, 1989. https://doi.org/10.1214/aos/1176347395