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Conditional Markov chain and its application in economic time series analysis

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  • Bai, Jushan
  • Wang, Peng

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.

Suggested Citation

  • Bai, Jushan & Wang, Peng, 2011. "Conditional Markov chain and its application in economic time series analysis," MPRA Paper 33369, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:33369
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    References listed on IDEAS

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    1. Olivier Blanchard & John Simon, 2001. "The Long and Large Decline in U.S. Output Volatility," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 32(1), pages 135-174.
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    3. Amisano, Gianni & Geweke, John, 2007. "Hierarchical Markov normal mixture models with applications to financial asset returns," Working Paper Series 831, European Central Bank.
    4. Margaret M. McConnell & Gabriel Perez-Quiros, 2000. "Output fluctuations in the United States: what has changed since the early 1980s?," Proceedings, Federal Reserve Bank of San Francisco.
    5. Charles R. Nelson, 2000. "Output fluctuations in the United States: what has changed since the early 1980s? comments," Proceedings, Federal Reserve Bank of San Francisco.
    6. Emi Nakamura & Jón Steinsson & Robert Barro & José Ursúa, 2013. "Crises and Recoveries in an Empirical Model of Consumption Disasters," American Economic Journal: Macroeconomics, American Economic Association, vol. 5(3), pages 35-74, July.
    7. Kim, Chang-Jin & Nelson, Charles R & Piger, Jeremy, 2004. "The Less-Volatile U.S. Economy: A Bayesian Investigation of Timing, Breadth, and Potential Explanations," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 80-93, January.
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    Citations

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    Cited by:

    1. Stéphane GOUTTE & Benteng Zou, 2011. "Foreign exchange rates under Markov Regime switching model," CREA Discussion Paper Series 11-16, Center for Research in Economic Analysis, University of Luxembourg.
    2. 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.
    3. 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.
    4. Troy A. Davig, 2008. "Detecting recessions in the Great Moderation: a real-time analysis," Economic Review, Federal Reserve Bank of Kansas City, issue Q IV, pages 5-33.
    5. Goutte, Stéphane, 2014. "Conditional Markov regime switching model applied to economic modelling," Economic Modelling, Elsevier, vol. 38(C), pages 258-269.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Stéphane Goutte & Benteng Zou, 2012. "Continuous time regime switching model applied to foreign exchange rate," Working Papers hal-00643900, HAL.
    11. Chevallier, Julien, 2011. "A model of carbon price interactions with macroeconomic and energy dynamics," Energy Economics, Elsevier, vol. 33(6), pages 1295-1312.
    12. Sylvia Kaufmann, 2016. "Hidden Markov models in time series, with applications in economics," Working Papers 16.06, Swiss National Bank, Study Center Gerzensee.
    13. 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

    Keywords

    Markov regime switching; Conditional Markov chain;

    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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