Inference on filtered and smoothed probabilities in Markov-switching autoregressive models

© 2018. The authors. This document is made available under the CC-BY-NC 4.0 license http://creativecommons.org/licenses/by-nc /4.0/ This document is the submitted version of a published work that appeared in final form in Journal of Business & Economic Statistics.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