Abstract:
Hamilton's (1989) nonlinear Markovian filter is extend to allow state transitions to be duration dependent. Restrictions are imposed on the state transition matrix associated with a T-order Markov system such that the corresponding first-order conditional transition probabilities are functions of both the inferred current state and also the number of periods the process has been in that state. High-order structure is parsimoniously summarized by the inferred duration variable. Applied to U.S. post-war real GNP growth rates, we obtain evidence in support of nonlinearity, asymmetry between recessions and expansions, as well as strong duration dependence for recessions but not for expansions
