Asymptotic properties of the maximum likelihood estimator in regime-switching models with time-varying transition probabilities
研究了时变转移概率体制转换模型中最大似然估计量的一致性和渐近正态性，并在误设定下证明了估计量的一致性，通过模拟和实证比较了不同经济指标对美国工业生产的描述能力。
Summary Time-varying transition probability (TVTP) regime-switching models extend the constant regime transition probability in Markov-switching models to include information from observations. We show consistency and asymptotic normality of the maximum likelihood estimator (MLE) in general TVTP regime-switching models where the conditional distribution of $Y_t$ depends on lagged regimes. Consistency of the MLE is also shown under misspecification. The assumptions are verified in regime-switching autoregressive models with widely applied TVTP specifications. A simulation study examines the finite-sample distributions of the MLE and compares the asymptotic variance estimates constructed from the Hessian matrix and the outer product of the score. The simulation results favour the latter. As an empirical example, we compare three leading economic indicators in terms of describing U.S. industrial production.