Date-stamping multiple bubble regimes

Identifying the start and end dates of explosive bubble regimes has become a prominent issue in the econometric literature. Recent research has demonstrated the advantage of a model-based minimum sum of squared residuals estimator, combined with Bayesian Information Criterion model selection, over recursive unit root testing methods in providing accurate date estimates for a single explosive regime. However, in the context of multiple bubbles, a large number of models are possible, making such a model-based method unappealing. In this paper, we propose a two-step procedure for dating multiple explosive regimes. First, recursive unit root tests are used to identify a ‘date window’ in which an explosive episode starts and ends. Second, a model-based BIC approach is used to precisely estimate the regime change points within each date window. In addition, our method allows us to distinguish between different types of explosive episode, such as whether or not each explosive regime crashes before reverting back to a unit root process, and date any crash regimes. Monte Carlo simulations highlight the effectiveness of our procedure when compared to existing methods of dating. The value of the new methodology is also demonstrated through an empirical application to housing markets.