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Testing the Number of Regimes in Markov Regime Switching Models

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  • Hiroyuki Kasahara
  • Katsumi Shimotsu
Abstract
Markov regime switching models have been used in numerous empirical studies in economics and finance. However, the asymptotic distribution of the likelihood ratio test statistic for testing the number of regimes in Markov regime switching models has been an unresolved problem. This paper derives the asymptotic distribution of the likelihood ratio test statistic for testing the null hypothesis of $M_0$ regimes against the alternative hypothesis of $M_0 + 1$ regimes for any $M_0 \geq 1$ both under the null hypothesis and under local alternatives. We show that the contiguous alternatives converge to the null hypothesis at a rate of $n^{-1/8}$ in regime switching models with normal density. The asymptotic validity of the parametric bootstrap is also established.

Suggested Citation

  • Hiroyuki Kasahara & Katsumi Shimotsu, 2018. "Testing the Number of Regimes in Markov Regime Switching Models," Papers 1801.06862, arXiv.org, revised Jan 2018.
    • Handle: RePEc:arx:papers:1801.06862
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    References listed on IDEAS

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    1. Leroux, Brian G., 1992. "Maximum-likelihood estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 127-143, February.
    2. Jin Seo Cho & Halbert White, 2007. "Testing for Regime Switching," Econometrica, Econometric Society, vol. 75(6), pages 1671-1720, November.
    3. Andrew Ang & Allan Timmermann, 2012. "Regime Changes and Financial Markets," Annual Review of Financial Economics, Annual Reviews, vol. 4(1), pages 313-337, October.
    4. Vadim Marmer, 2008. "Testing the null hypothesis of no regime switching with an application to GDP growth rates," Empirical Economics, Springer, vol. 35(1), pages 101-122, August.
    5. Andrew Ang & Geert Bekaert, 2002. "International Asset Allocation With Regime Shifts," The Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1137-1187.
    6. Andrew V. Carter & Douglas G. Steigerwald, 2012. "Testing for Regime Switching: A Comment," Econometrica, Econometric Society, vol. 80(4), pages 1809-1812, July.
    7. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
    8. Jiahua Chen & Pengfei Li & Yuejiao Fu, 2012. "Inference on the Order of a Normal Mixture," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1096-1105, September.
    9. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    10. Kahn, James A. & Rich, Robert W., 2007. "Tracking the new economy: Using growth theory to detect changes in trend productivity," Journal of Monetary Economics, Elsevier, vol. 54(6), pages 1670-1701, September.
    11. J. B. Taylor & Harald Uhlig (ed.), 2016. "Handbook of Macroeconomics," Handbook of Macroeconomics, Elsevier, edition 1, volume 2, number 2.
    12. Jean-Marie Dufour & Richard Luger, 2017. "Identification-robust moment-based tests for Markov switching in autoregressive models," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 713-727, October.
    13. Lee, Lung-Fei & Chesher, Andrew, 1986. "Specification testing when score test statistics are identically zero," Journal of Econometrics, Elsevier, vol. 31(2), pages 121-149, March.
    14. Frank Schorfheide, 2005. "Learning and Monetary Policy Shifts," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 392-419, April.
    15. Christopher A. Sims & Tao Zha, 2006. "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, American Economic Association, vol. 96(1), pages 54-81, March.
    16. 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.
    17. Marine Carrasco & Liang Hu & Werner Ploberger, 2014. "Optimal Test for Markov Switching Parameters," Econometrica, Econometric Society, vol. 82(2), pages 765-784, March.
    18. Chen, Xiaohong & Ponomareva, Maria & Tamer, Elie, 2014. "Likelihood inference in some finite mixture models," Journal of Econometrics, Elsevier, vol. 182(1), pages 87-99.
    19. Jiaying Gu & Roger Koenker & Stanislav Volgushev, 2017. "Testing for homogeneity in mixture models," CeMMAP working papers CWP39/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    20. Hiroyuki Kasahara & Katsumi Shimotsu, 2015. "Testing the Number of Components in Normal Mixture Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1632-1645, December.
    21. James Morley & Jeremy Piger, 2012. "The Asymmetric Business Cycle," The Review of Economics and Statistics, MIT Press, vol. 94(1), pages 208-221, February.
    22. 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.
    23. Okimoto, Tatsuyoshi, 2008. "New Evidence of Asymmetric Dependence Structures in International Equity Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 43(3), pages 787-815, September.
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    Cited by:

    1. Kasahara, Hiroyuki & Shimotsu, Katsumi, 2019. "Asymptotic properties of the maximum likelihood estimator in regime switching econometric models," Journal of Econometrics, Elsevier, vol. 208(2), pages 442-467.
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    3. Gabriel Rodriguez-Rondon & Jean-Marie Dufour, 2024. "MSTest: An R-Package for Testing Markov Switching Models," Papers 2411.08188, arXiv.org.
    4. Shaw, Charles, 2018. "Regime-Switching And Levy Jump Dynamics In Option-Adjusted Spreads," MPRA Paper 94154, University Library of Munich, Germany, revised 27 May 2019.
    5. Meitz, Mika & Saikkonen, Pentti, 2021. "Testing for observation-dependent regime switching in mixture autoregressive models," Journal of Econometrics, Elsevier, vol. 222(1), pages 601-624.

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