Regime Switching with Time-Varying Transition Probabilities

By Francis X. Diebold, Joon-Haeng Lee, G. Weinbach. Business Cycles, 2020

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Models incorporating nonlinearities associated with regime switching have a long tradition in empirical macroeconomics and dynamic econometrics. Key methodological contributions include the early work of Quandt (1958) and Goldfeld and Quandt (1973) and the more recent work of Hamilton (1990). Recent substantive applications include Hamilton (1988) (interest rates), Hamilton (1989) (aggregate output), Cecchetti, Lam and Mark (1990) and Abel (1992) (stock returns), and Engel and Hamilton (1990) (exchange rates), among many others. Our attention here focuses on Hamilton's Markov switching model, which has become very popular. In Hamilton's model, time-series dynamics are governed by a finite-dimensional parameter vector, which switches (potentially each period) depending upon which of two states is realised, with state transitions governed by a first-order Markov process with constant transition probabilities. Although the popularity of Hamilton's model is well deserved, it nevertheless incorporates a potentially severely binding constraint, the constancy of state transition probabilities. Economic considerations suggest the desirability of allowing the transition probabilities to vary. As an example, consider the process of exchange rate revaluation. It is plausible that the likelihood of exchange rate revaluation increases under progressively more severe overor undervaluation on the basis of economic fundamentals, and certainly, one would not want to exclude that possibility from the outset.

Subfields: Finance, Statistical and Nonlinear Physics

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