Inference on Filtered and Smoothed Probabilities in Markov-Switching Autoregressive Models
推导了马尔可夫转换自回归模型中滤波和平滑概率的渐近分布理论，并应用于美国GDP增长率和实际利率数据，为识别经济周期和利率制度提供置信区间。
We derive a statistical theory that provides useful asymptotic approximations to the distributions of the single inferences of filtered and smoothed probabilities, derived from time series characterized by Markov-switching dynamics. We show that the uncertainty in these probabilities diminishes when the states are separated, the variance of the shocks is low, and the time series or the regimes are persistent. As empirical illustrations of our approach, we analyze the U.S. GDP growth rates and the U.S. real interest rates. For both models, we illustrate the usefulness of the confidence intervals when identifying the business cycle phases and the interest rate regimes.