Sample path properties of an explosive double autoregressive model

This article studies sample path properties of an explosive double autoregressive (DAR) model. After suitable renormalization, it is shown that the sample path converges weakly to a geometric Brownian motion. This further strengthens our understanding of sample paths of nonstationary DAR processes. The obtained results can be extended to nonstationary random coefficient autoregressive (RCA) models. Simulation studies are carried out to support our results.