Inference on Filtered and Smoothed Probabilities in Markov-Switching Autoregressive Models |
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| Authors: | Rocio Alvarez Maximo Camacho Manuel Ruiz |
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| Affiliation: | 1. Facultad de Economía y Negocios, Universidad Central de Chile, Santiago, Región Metropolitana, Chile (rocio.alvareza@ucentral.cl);2. Departamento de Métodos Cuantítativos para la Economía y la Empresa, Facultad de Economia y Empresa, Universidad de Murcia, 30100 Murcia, Spain (mcamacho@um.es);3. Departamento de Métodos Cuantítativos e Informáticos, Facultad de Ciencias de la Empresa, Universidad Politécnica de Cartagena, 30202 Cartagena, Murcia, Spain (manuel.ruiz@upct.es) |
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| Abstract: | ABSTRACTWe 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. |
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| Keywords: | Business cycles Markov switching Time series. |
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