Asymptotic validity of the bootstrap is established for the least squares estimate of the parameter of an explosive first-order autoregressive process. It is noted that nonnormal limit distributions are obtained for both the traditional and the bootstrap estimates. The theoretical bootstrap validity results are supported by appropriate simulation.
"Bootstrapping Explosive Autoregressive Processes." Ann. Statist. 17 (4) 1479 - 1486, December, 1989. https://doi.org/10.1214/aos/1176347376