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A Bayesian Approach to Testing for Markov Switching in Univariate and Dynamic Factor Models

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  • Chang-Jin Kim
  • Charles Nelson
Abstract
Though Hamilton's (1989) Markov-switching model has been widely estimated in various contexts, formal testing for Markov-switching is not straightforward. Univariate tests in the classical framework by Hansen (1992) and Garcia (1998) do not reject the linear model for GDP. We present Bayesian tests for Markov-switching in both univariate and multivariate settings based on sensitivity of the posterior probability to the prior. We find that evidence for Markov-switching, and thus the business cycle asymmetry, is stronger in a switching version of the dynamic factor model of Stock and Watson (1991) than it is for GDP by itself.
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Suggested Citation

  • Chang-Jin Kim & Charles Nelson, 1998. "A Bayesian Approach to Testing for Markov Switching in Univariate and Dynamic Factor Models," Discussion Papers in Economics at the University of Washington 0059, Department of Economics at the University of Washington.
    • Handle: RePEc:fth:washer:0059
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    1. Hansen, Bruce E, 1992. "The Likelihood Ratio Test under Nonstandard Conditions: Testing the Markov Switching Model of GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 61-82, Suppl. De.
    2. Kim, Chang-Jin & Nelson, Charles R, 1999. "Friedman's Plucking Model of Business Fluctuations: Tests and Estimates of Permanent and Transitory Components," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 31(3), pages 317-334, August.
    3. Potter, Simon M, 1995. "A Nonlinear Approach to US GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(2), pages 109-125, April-Jun.
    4. Zivot, E., 1993. "A Bayesian Analysis of the Unit Root Hypothesis Within an Unobserved Components Model," Discussion Papers in Economics at the University of Washington 93-15, Department of Economics at the University of Washington.
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    10. Arthur F. Burns & Wesley C. Mitchell, 1946. "Measuring Business Cycles," NBER Books, National Bureau of Economic Research, Inc, number burn46-1.
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    12. Dale J. Poirier, 1995. "Intermediate Statistics and Econometrics: A Comparative Approach," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262161494, April.
    13. 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.
    14. Friedman, Milton, 1993. "The "Plucking Model" of Business Fluctuations Revisited," Economic Inquiry, Western Economic Association International, vol. 31(2), pages 171-177, April.
    15. Koop, Gary & Potter, Simon M., 1998. "Bayes factors and nonlinearity: Evidence from economic time series1," Journal of Econometrics, Elsevier, vol. 88(2), pages 251-281, November.
    16. Filardo, Andrew J. & Gordon, Stephen F., 1998. "Business cycle durations," Journal of Econometrics, Elsevier, vol. 85(1), pages 99-123, July.
    17. Zivot, Eric, 1994. "A Bayesian Analysis Of The Unit Root Hypothesis Within An Unobserved Components Model," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 552-578, August.
    18. Chang-Jin Kim & Charles R. Nelson, 1998. "Business Cycle Turning Points, A New Coincident Index, And Tests Of Duration Dependence Based On A Dynamic Factor Model With Regime Switching," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 188-201, May.
    19. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    20. Garcia, Rene, 1998. "Asymptotic Null Distribution of the Likelihood Ratio Test in Markov Switching Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(3), pages 763-788, August.
    21. Chang-Jin Kim & Charles R. Nelson, 1999. "Has The U.S. Economy Become More Stable? A Bayesian Approach Based On A Markov-Switching Model Of The Business Cycle," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 608-616, November.
    22. Perron, Pierre, 1990. "Testing for a Unit Root in a Time Series with a Changing Mean," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 153-162, April.
    23. Chang-Jin Kim & Charles R. Nelson, 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262112388, April.
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    1. Kim, Chang-Jin & Piger, Jeremy, 2002. "Common stochastic trends, common cycles, and asymmetry in economic fluctuations," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1189-1211, September.
    2. Wang, Hong & Forbes, Catherine S. & Fenech, Jean-Pierre & Vaz, John, 2020. "The determinants of bank loan recovery rates in good times and bad – New evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 177(C), pages 875-897.
    3. Kagraoka, Yusho & Moussa, Zakaria, 2013. "Quantitative easing, credibility and the time-varying dynamics of the term structure of interest rate in Japan," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 25(C), pages 181-201.
    4. Andrew Binning & Junior Maih, 2015. "Sigma point filters for dynamic nonlinear regime switching models," Working Paper 2015/10, Norges Bank.
    5. Raslan Alzubi & Mustafa Caglayan & Kostas Mouratidis, 2017. "The Risk-Taking Channel in the US: A GVAR Approach," Working Papers 2017009, The University of Sheffield, Department of Economics.
    6. Chang-Jin Kim & Jeremy M. Piger & Richard Startz, 2007. "The Dynamic Relationship between Permanent and Transitory Components of U.S. Business Cycles," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(1), pages 187-204, February.
    7. Panagiotis Petris & George Dotsis & Panayotis Alexakis, 2022. "Bubble tests in the London housing market: A borough level analysis," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(1), pages 1044-1063, January.
    8. Wahyudi, Imam & Luxianto, Rizky & Iwani, Niken & Sulung, Liyu Adhika Sari, 2008. "Early Warning System in ASEAN Countries Using Capital Market Index Return: Modified Markov Regime Switching Model," MPRA Paper 59723, University Library of Munich, Germany, revised 16 Jul 2010.
    9. Issler, João Victor & Notini, Hilton Hostalacio, 2016. "Estimating Brazilian Monthly GDP: a State-Space Approach," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 70(1), March.
    10. Zakaria Moussa, 2016. "How big is the comeback? Japanese exchange rate pass-through assessed by time-varying FAVAR," Post-Print hal-03714934, HAL.
    11. de Mello, Luiz & Moccero, Diego, 2011. "Monetary policy and macroeconomic stability in Latin America: The cases of Brazil, Chile, Colombia and Mexico," Journal of International Money and Finance, Elsevier, vol. 30(1), pages 229-245, February.
    12. Tan, Siow-Hooi & Habibullah, Muzafar Shah, 2007. "Business cycles and monetary policy asymmetry: An investigation using Markov-switching models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 297-306.
    13. Xiongfeng Pan & Jing Zhang & Changyu Li & Rong Quan & Bin Li, 2018. "Exploring Dynamic Impact of Foreign Direct Investment on China’s CO $$_{2}$$ 2 Emissions Using Markov-Switching Vector Error Correction Model," Computational Economics, Springer;Society for Computational Economics, vol. 52(4), pages 1139-1151, December.
    14. Jacob Boudoukh & Matthew Richardson & Tom Smith & Robert Whitelaw, 1999. "Regime Shifts and Bond Returns," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-010, New York University, Leonard N. Stern School of Business-.
    15. Sugita, Katsuhiro, 2008. "Bayesian analysis of a Markov switching temporal cointegration model," Japan and the World Economy, Elsevier, vol. 20(2), pages 257-274, March.
    16. Chang-Jin Kim & Jeremy M. Piger & Richard Startz, 2001. "Permanent and transitory components of business cycles: their relative importance and dynamic relationship," International Finance Discussion Papers 703, Board of Governors of the Federal Reserve System (U.S.).
    17. Zhiqiang HU & Yizhu WANG, 2013. "The IPO Cycles in China's A-share IPO Market: Detection Based on a Three Regimes Markov Switching Model," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(3), pages 115-131, October.
    18. Rafael Ravnik, 2014. "Short-Term Forecasting of GDP under Structural Changes," Working Papers 40, The Croatian National Bank, Croatia.
    19. López-Herrera, Francisco & Ortiz-Arango, Francisco & Venegas-Martínez, Francisco, 2011. "Modelado de la volatilidad del Índice de Precios y Cotizaciones de la Bolsa Mexicana de Valores con cambios markovianos de régimen," Sección de Estudios de Posgrado e Investigación de la Escuela Superios de Economía del Instituto Politécnico Nacional, in: Perrotini-Hernández, Ignacio (ed.), Crecimiento y Desarrollo Económico en México, volume 1, chapter 10, pages 153-164, Escuela Superior de Economía, Instituto Politécnico Nacional.
    20. Geweke, John, 2007. "Interpretation and inference in mixture models: Simple MCMC works," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3529-3550, April.
    21. Zakaria Moussa, 2016. "How big is the comeback? Japanese exchange rate pass-through assessed by Time-Varying FAVAR," Working Papers hal-01282811, HAL.
    22. Raslan Alzuabi & Mustafa Caglayan & Kostas Mouratidis, 2021. "The risk‐taking channel in the United States: A GVAR approach," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(4), pages 5826-5849, October.

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