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Conditional Markov chain and its application in economic time series analysis

Author

Listed:
  • Jushan Bai
  • Peng Wang

Abstract

Motivated by the great moderation in major U.S. macroeconomic time series, we formulate the regime switching problem through a conditional Markov chain. We model the long-run volatility change as a recurrent structure change, while short-run changes in the mean growth rate as regime switches. Both structure and regime are unobserved. The structure is assumed to be Markovian. Conditioning on the structure, the regime is also Markovian, whose transition matrix is structure-dependent. This formulation imposes interpretable restrictions on the Hamilton Markov switching model. Empirical studies show that this restricted model well identifies both short-run regime switches and long-run structure changes in the U.S. macroeconomic data.
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Suggested Citation

  • Jushan Bai & Peng Wang, 2011. "Conditional Markov chain and its application in economic time series analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(5), pages 715-734, August.
    • Handle: RePEc:wly:japmet:v:26:y:2011:i:5:p:715-734
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    Cited by:

    1. Leiva-Leon, Danilo, 2013. "A New Approach to Infer Changes in the Synchronization of Business Cycle Phases," MPRA Paper 54452, University Library of Munich, Germany.
    2. Shu-Ping Shi, 2013. "Specification sensitivities in the Markov-switching unit root test for bubbles," Empirical Economics, Springer, vol. 45(2), pages 697-713, October.
    3. Catherine Doz & Laurent Ferrara & Pierre-Alain Pionnier, 2025. "Switching Macroeconomic Growth and Volatility: Evidence from a Mean-Variance Markov-Switching Dynamic Factor Model," PSE Working Papers halshs-02443364, HAL.
    4. Danilo Leiva-Leon, 2017. "Measuring Business Cycles Intra-Synchronization in US: A Regime-switching Interdependence Framework," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(4), pages 513-545, August.
    5. Stéphane Goutte & Benteng Zou, 2012. "Continuous time regime switching model applied to foreign exchange rate," Working Papers hal-00643900, HAL.
    6. Printechapat, Tanes & Aiewsakun, Pakorn & Krityakierne, Tipaluck, 2025. "Caged Markov process – A continuous-time framework for modeling a constrained Markov process within a freely-evolving Markov process," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 230(C), pages 350-369.
    7. Sylvain Mignot & Annick Vignes, 2020. "The Many Faces of Agent-Based Computational Economics: Ecology of Agents, Bottom-Up Approaches and Paradigm Shift [Les modèles multi-agents en économie, entre agents hétérogènes, approches bottom-u," Post-Print hal-02956172, HAL.
    8. Stéphane GOUTTE & Benteng Zou, 2011. "Foreign exchange rates under Markov Regime switching model," DEM Discussion Paper Series 11-16, Department of Economics at the University of Luxembourg.
    9. Chang, Kuang-Liang, 2016. "Does the return-state-varying relationship between risk and return matter in modeling the time series process of stock return?," International Review of Economics & Finance, Elsevier, vol. 42(C), pages 72-87.
    10. Troy Davig, 2008. "Detecting recessions in the Great Moderation: a real-time analysis," Economic Review, Federal Reserve Bank of Kansas City, vol. 93(Q IV), pages 5-33.
    11. Kenneth Martínez & David Claudio & Jasmina Burek, 2025. "Modeling resilience and survivability as stochastic processes with techno-human-economic systems under stress," Journal of Computational Social Science, Springer, vol. 8(1), pages 1-42, February.
    12. Goutte, Stéphane, 2014. "Conditional Markov regime switching model applied to economic modelling," Economic Modelling, Elsevier, vol. 38(C), pages 258-269.
    13. Chevallier, Julien, 2011. "Evaluating the carbon-macroeconomy relationship: Evidence from threshold vector error-correction and Markov-switching VAR models," Economic Modelling, Elsevier, vol. 28(6), pages 2634-2656.
    14. Raphaël Homayoun Boroumand & Stéphane Goutte & Simon Porcher & Thomas Porcher, 2014. "A Conditional Markov Regime Switching Model to Study Margins: Application to the French Fuel Retail Markets," Working Papers hal-01090837, HAL.
    15. Chevallier, Julien, 2011. "A model of carbon price interactions with macroeconomic and energy dynamics," Energy Economics, Elsevier, vol. 33(6), pages 1295-1312.
    16. Sylvia Kaufmann, 2016. "Hidden Markov models in time series, with applications in economics," Working Papers 16.06, Swiss National Bank, Study Center Gerzensee.
    17. Gilbert Mbara, 2017. "Business Cycle Dating after the Great Moderation: A Consistent Two – Stage Maximum Likelihood Method," Working Papers 2017-13, Faculty of Economic Sciences, University of Warsaw.

    More about this item

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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