Hamilton's nonlinear Markovian filter is extended to allow state transitions to be duration dependent. Restrictions are imposed on the state transition matrix associated with a τ-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. postwar real GNP growth rates, we obtain evidence in support of nonlinearity, asymmetry between recessions and expansions, and duration dependence for recessions but not for expansions.
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