Identifying Speculative Bubbles with an Infinite Hidden Markov Model

This paper proposes an infinite hidden Markov model (iHMM) to detect, date stamp, and estimate speculative bubbles. Three features make this new approach attractive to practitioners. first, the iHMM is capable of capturing the nonlinear dynamics of different types of bubble behaviors as it allows an infinite number of regimes. Second, the implementation of this procedure is straightforward as the detection, dating, and estimation of bubbles are done simultaneously in a coherent Bayesian framework. Third, the iHMM, by assuming hierarchical structures, is parsimonious and superior in out-of-sample forecast. Two empirical applications are presented: one to the Argentinian money base, exchange rate, and consumer price from January 1983 to November 1989; and the other to the U.S. oil price from April 1983 to December 2010. We find prominent results, which have not been discovered by the existing finite hidden Markov model. Model comparison shows that the iHMM is strongly supported by the predictive likelihood.