This paper addresses the problem of testing for the presence of a stochastic bubble in a time series in the case that the bubble is periodically collapsing so that the asset price keeps returning to the level implied by the market fundamentals. As this is essentially a problem of identifying the collapsing periods from the expanding ones, we propose using a generalization of the Dickey±Fuller test procedure which makes use of the class of Markov regime-switching models. The potential of the new methodology is illustrated via simulation, and an empirical example is given. Copyright #1999 John Wiley & Sons, Ltd.
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