论文标题
具有随时间变化的过渡概率
Asymptotic Properties of the Maximum Likelihood Estimator in Regime-Switching Models with Time-Varying Transition Probabilities
论文作者
论文摘要
我们证明了时变过渡概率（TVTP）制度模型中最大似然估计器（MLE）的渐近性能。这类模型通过包括观测值的信息，将马尔可夫开关模型中的恒定状态转变概率扩展到了随时间变化的概率。此证明中的一个重要特征是在观测值中条件的制度过程的混合速率，这是由于时间变化的过渡概率而变化的时间。一致性和渐近正态性来自混合速率几乎确定性的几何衰减结合。这些假设在具有广泛应用的TVTP规格的自回归模型中得到了验证。一项仿真研究检查了MLE的有限样本分布，并比较了根据Hessian矩阵构建的渐近方差的估计值和分数的外产物。模拟结果有利于后者。作为一个经验例子，我们在描述美国工业生产方面比较了三个领先的经济指标。
We prove the asymptotic properties of the maximum likelihood estimator (MLE) in time-varying transition probability (TVTP) regime-switching models. This class of models extends the constant regime transition probability in Markov-switching models to a time-varying probability by including information from observations. An important feature in this proof is the mixing rate of the regime process conditional on the observations, which is time varying owing to the time-varying transition probabilities. Consistency and asymptotic normality follow from the almost deterministic geometrically decaying bound of the mixing rate. 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 estimates of the asymptotic variance 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.
