Testing for a bubble with a stochastically varying explosive coefficient

In this article, we test for a bubble in a model with a random explosive autoregressive coefficient. We consider two local alternatives and find that versions of recursive stochastic unit root tests are more powerful when facing a randomly explosive process than the recursive right-tailed ADF tests, whereas the latter performs better in a model with a non-stochastic coefficient. We then propose the union of rejections strategy using the recursive right-tailed ADF and stochastic unit root tests. We examine the finite sample properties of the proposed tests using Monte Carlo simulations and observe that the test based on the union of rejections strategy is the second-best, and its power is close to the best one in most cases.