Abstract

In this article, we investigate the tests for a bubble in a model with the randomly explosive autoregressive coefficient. We consider the two local alternatives and find that versions of recursive stochastic unit root tests are more powerful against a randomly explosive process than the recursive right-tailed ADF tests, whereas the latter perform better for the model with the nonstochastic coefficient. We then propose the union of rejections strategy using the recursive right-tailed ADF and stochastic unit root tests. The finite sample property of the proposed tests is investigated by Monte Carlo simulations and it is observed 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.