A Markov Regime-Switching Model with Time-Varying Transition Probabilities for Identifying Asset Price Bubbles

Abstract

In this paper, a Markov regime-switching model with time-varying transition probabilities is developed to identify asset price bubbles in the S&P 500 index. The model nests two different methodologies; a state-dependent regime-switching model and a Markov regime-switching model. Three bubble regimes are identified; dormant, explosive, and collapsing. Time-varying transition probabilities are specified for each of the nine possible transitions in the Markov regime-switching model. Estimation of the model is done using conditional maximum likelihood with the Hamilton filter. Results show that transition probabilities depend significantly on trading volume and relative size of the bubble. Overall, the model works well in detecting multiple bubbles in the S&P 500 between January 1888 and May 2010. Explosive bubbles tend to immediately precede recession periods, while collapsing bubbles tend to coincide with recession periods.