Duration-Dependent Transitions in a Markov Model of U.S. GNP Growth
扩展了Hamilton的非线性马尔可夫滤波器，允许状态转换概率依赖于当前状态已持续的时期数，并应用于美国战后实际GNP增长率，发现衰退具有强持续时间依赖性而扩张则没有。
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