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Bayesian Inference for Periodic Regime-Switching Models

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  • Eric Ghysels
  • Robert E. McCulloch
  • Ruey S. Tsay

Abstract

We present a general class of nonlinear time series Markov regime-switching models for seasonal data which may exhibit periodic features in the hidden Markov process as well as in the laws of motion in each of the regimes. This class of models allows for nontrivial dependencies between seasonal, cyclical and long-term patterns in the data. To overcome the competitional burden we adopt a Bayesian approach to estimation and inference. This paper contains two empirical examples as illustration, one using housing starts data while the other covers U.S. post WWII individual production. Nous présentons une classe générale de modèles non-linéaires avec changement de régime Markovienne. Les modèles proposés permettent d'avoir une structure périodique pour la chaîne de Markov ainsi que des effets saisonniers dans chaqu'un des régimes. La classe de structure proposée permet d'avoir des interdépendences entre les fluctuationssaisonnières, les cycles d'affaire et la composante de croissance. Une méthode Baysienne basée sur le principe de l'échantillonage de Gibbs est utilisée pour estimation et interférence. Deux exemples empiriques sont fournis, un premier utilisant des séries de mise en chantier de0501sons, tandis que le second couvre la production industrielle aux États-Unis.

Suggested Citation

  • Eric Ghysels & Robert E. McCulloch & Ruey S. Tsay, 1994. "Bayesian Inference for Periodic Regime-Switching Models," CIRANO Working Papers 94s-15, CIRANO.
    • Handle: RePEc:cir:cirwor:94s-15
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    References listed on IDEAS

    as
    1. Eric Ghysels, 1993. "A time series model with periodic stochastic regime switching," Discussion Paper / Institute for Empirical Macroeconomics 84, Federal Reserve Bank of Minneapolis.
    2. Ghysels, Eric, 1994. "On the Periodic Structure of the Business Cycle," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 289-298, July.
    3. Robert E. McCulloch & Ruey S. Tsay, 1994. "Statistical Analysis Of Economic Time Series Via Markov Switching Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(5), pages 523-539, September.
    4. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    5. Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March.
    6. Neftci, Salih N, 1984. "Are Economic Time Series Asymmetric over the Business Cycle?," Journal of Political Economy, University of Chicago Press, vol. 92(2), pages 307-328, April.
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    1. Bailliu, Jeannine & Dib, Ali & Kano, Takashi & Schembri, Lawrence, 2014. "Multilateral adjustment, regime switching and real exchange rate dynamics," The North American Journal of Economics and Finance, Elsevier, vol. 27(C), pages 68-87.
    2. Smith, Aaron & Naik, Prasad A. & Tsai, Chih-Ling, 2006. "Markov-switching model selection using Kullback-Leibler divergence," Journal of Econometrics, Elsevier, vol. 134(2), pages 553-577, October.
    3. Christiano, Lawrence J. & Todd, Richard M., 2002. "The conventional treatment of seasonality in business cycle analysis: does it create distortions?," Journal of Monetary Economics, Elsevier, vol. 49(2), pages 335-364, March.
    4. Jaehee Kim & Sooyoung Cheon, 2010. "A Bayesian regime‐switching time‐series model," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 365-378, September.
    5. Aknouche, Abdelhakim, 2024. "Periodically homogeneous Markov chains: The discrete state space case," MPRA Paper 122287, University Library of Munich, Germany.
    6. Zhao-Hua Lu & Sy-Miin Chow & Nilam Ram & Pamela M. Cole, 2019. "Zero-Inflated Regime-Switching Stochastic Differential Equation Models for Highly Unbalanced Multivariate, Multi-Subject Time-Series Data," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 611-645, June.
    7. Carvalho, Alexandre X. & Tanner, Martin A., 2007. "Modelling nonlinear count time series with local mixtures of Poisson autoregressions," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5266-5294, July.

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    More about this item

    Keywords

    Markov switching; Periodic models; Seasonality; Gibbs sampler; Modèles à changement de régime ; Structure périodique ; Saisonnalité ; Échantillonage de Gibbs;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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