IDEAS home Printed from https://ideas.repec.org/a/bpj/sndecm/v28y2024i2p177-199n1.html
   My bibliography  Save this article

Markov-Switching Models with Unknown Error Distributions: Identification and Inference Within the Bayesian Framework

Author

Listed:
  • Hwu Shih-Tang

    (Department of Economics, California State Polytechnic University, Pomona, USA)

  • Kim Chang-Jin

    (Department of Economics, University of Washington, Seattle, USA)

Abstract

The basic Markov-switching model has been extended in various ways ever since the seminal work of Hamilton (1989. “A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle.” Econometrica 57: 357–84). However, the estimation of Markov-switching models in the literature has relied upon parametric assumptions on the distribution of the error term. In this paper, we present a Bayesian approach for estimating Markov-switching models with unknown and potentially non-normal error distributions. We approximate the unknown distribution of the error term by the Dirichlet process mixture of normals, in which the number of mixtures is treated as a parameter to estimate. In doing so, we pay special attention to the identification of the model. We then apply the proposed model and MCMC procedure to the growth of the postwar U.S. industrial production index. Our model can effectively control for irregular components that are not related to business conditions. This leads to sharp and accurate inferences on recession probabilities.

Suggested Citation

  • Hwu Shih-Tang & Kim Chang-Jin, 2024. "Markov-Switching Models with Unknown Error Distributions: Identification and Inference Within the Bayesian Framework," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 28(2), pages 177-199, April.
    • Handle: RePEc:bpj:sndecm:v:28:y:2024:i:2:p:177-199:n:1
    DOI: 10.1515/snde-2022-0055
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/snde-2022-0055
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/snde-2022-0055?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Luc Bauwens & Jean-François Carpantier & Arnaud Dufays, 2017. "Autoregressive Moving Average Infinite Hidden Markov-Switching Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 162-182, April.
    2. Hamilton, J.D., 2016. "Macroeconomic Regimes and Regime Shifts," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 163-201, Elsevier.
    3. Filardo, Andrew J, 1994. "Business-Cycle Phases and Their Transitional Dynamics," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 299-308, July.
    4. Chib, Siddhartha, 1998. "Estimation and comparison of multiple change-point models," Journal of Econometrics, Elsevier, vol. 86(2), pages 221-241, June.
    5. Yunjong Eo & Chang-Jin Kim, 2016. "Markov-Switching Models with Evolving Regime-Specific Parameters: Are Postwar Booms or Recessions All Alike?," The Review of Economics and Statistics, MIT Press, vol. 98(5), pages 940-949, December.
    6. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    7. Yong Song, 2014. "Modelling Regime Switching And Structural Breaks With An Infinite Hidden Markov Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(5), pages 825-842, August.
    8. Jan Bulla & Sascha Mergner & Ingo Bulla & André Sesboüé & Christophe Chesneau, 2011. "Markov-switching asset allocation: Do profitable strategies exist?," Journal of Asset Management, Palgrave Macmillan, vol. 12(5), pages 310-321, November.
    9. Kim, Chang-Jin, 1994. "Dynamic linear models with Markov-switching," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 1-22.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yong Song & Tomasz Wo'zniak, 2020. "Markov Switching," Papers 2002.03598, arXiv.org.
    2. Masaru Chiba, 2023. "Robust and efficient specification tests in Markov-switching autoregressive models," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 99-137, April.
    3. Maddalena Cavicchioli, 2021. "OLS Estimation of Markov switching VAR models: asymptotics and application to energy use," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(3), pages 431-449, September.
    4. Neville Francis & Michael T. Owyang & Daniel Soques, 2022. "Business Cycles across Space and Time," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 54(4), pages 921-952, June.
    5. Didier Nibbering & Richard Paap & Michel van der Wel, 2016. "A Bayesian Infinite Hidden Markov Vector Autoregressive Model," Tinbergen Institute Discussion Papers 16-107/III, Tinbergen Institute, revised 13 Oct 2017.
    6. Hamilton, J.D., 2016. "Macroeconomic Regimes and Regime Shifts," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 163-201, Elsevier.
    7. Antonio N. Bojanic, 2021. "A Markov-Switching Model of Inflation in Bolivia," Economies, MDPI, vol. 9(1), pages 1-18, March.
    8. Arnaud Dufays & Zhuo Li & Jeroen V.K. Rombouts & Yong Song, 2021. "Sparse change‐point VAR models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(6), pages 703-727, September.
    9. DESCHAMPS, Philippe J., 2016. "Bayesian Semiparametric Forecasts of Real Interest Rate Data," LIDAM Discussion Papers CORE 2016050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. van Os, Bram & van Dijk, Dick, 2024. "Accelerating peak dating in a dynamic factor Markov-switching model," International Journal of Forecasting, Elsevier, vol. 40(1), pages 313-323.
    11. Hou, Chenghan, 2017. "Infinite hidden markov switching VARs with application to macroeconomic forecast," International Journal of Forecasting, Elsevier, vol. 33(4), pages 1025-1043.
    12. Carstensen, Kai & Heinrich, Markus & Reif, Magnus & Wolters, Maik H., 2020. "Predicting ordinary and severe recessions with a three-state Markov-switching dynamic factor model," International Journal of Forecasting, Elsevier, vol. 36(3), pages 829-850.
    13. Magnus Reif, 2020. "Macroeconomics, Nonlinearities, and the Business Cycle," ifo Beiträge zur Wirtschaftsforschung, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, number 87, May.
    14. Marie Bessec, 2019. "Revisiting the transitional dynamics of business cycle phases with mixed-frequency data," Econometric Reviews, Taylor & Francis Journals, vol. 38(7), pages 711-732, August.
    15. Billio, Monica & Casarin, Roberto & Ravazzolo, Francesco & van Dijk, Herman K., 2012. "Combination schemes for turning point predictions," The Quarterly Review of Economics and Finance, Elsevier, vol. 52(4), pages 402-412.
    16. Anoek Castelein & Dennis Fok & Richard Paap, 2020. "A multinomial and rank-ordered logit model with inter- and intra-individual heteroscedasticity," Tinbergen Institute Discussion Papers 20-069/III, Tinbergen Institute.
    17. Terence C. Mills & Ping Wang, 2003. "Multivariate Markov Switching Common Factor Models for the UK," Bulletin of Economic Research, Wiley Blackwell, vol. 55(2), pages 177-193, April.
    18. Jin, Xin & Maheu, John M. & Yang, Qiao, 2022. "Infinite Markov pooling of predictive distributions," Journal of Econometrics, Elsevier, vol. 228(2), pages 302-321.
    19. Andrea Carriero & Massimiliano Marcellino, 2011. "Sectoral Survey‐based Confidence Indicators for Europe," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 73(2), pages 175-206, April.
    20. Samet G nay, 2015. "Markov Regime Switching Generalized Autoregressive Conditional Heteroskedastic Model and Volatility Modeling for Oil Returns," International Journal of Energy Economics and Policy, Econjournals, vol. 5(4), pages 979-985.

    More about this item

    Keywords

    label switching problem; identification condition; unknown error distribution; mixture of normals; semi-parametric Bayesian inference; Markov chain Monte Carlo;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:sndecm:v:28:y:2024:i:2:p:177-199:n:1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.