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Optimal Test for Markov Switching Parameters


  • Marine Carrasco
  • Liang Hu
  • Werner Ploberger


This paper proposes a class of optimal tests for the constancy of parameters in random coefficients models. Our testing procedure covers the class of Hamilton's models, where the parameters vary according to an unobservable Markov chain, but also applies to nonlinear models where the random coefficients need not be Markov. We show that the contiguous alternatives converge to the null hypothesis at a rate that is slower than the standard rate. Therefore, standard approaches do not apply. We use Bartlett‐type identities for the construction of the test statistics. This has several desirable properties. First, it only requires estimating the model under the null hypothesis where the parameters are constant. Second, the proposed test is asymptotically optimal in the sense that it maximizes a weighted power function. We derive the asymptotic distribution of our test under the null and local alternatives. Asymptotically valid bootstrap critical values are also proposed.

Suggested Citation

  • Marine Carrasco & Liang Hu & Werner Ploberger, 2014. "Optimal Test for Markov Switching Parameters," Econometrica, Econometric Society, vol. 82(2), pages 765-784, March.
  • Handle: RePEc:wly:emetrp:v:82:y:2014:i:2:p:765-784

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    Cited by:

    1. Yanlin Shi & Lingbing Feng & Tong Fu, 2020. "Markov Regime-Switching in-Mean Model with Tempered Stable Distribution," Computational Economics, Springer;Society for Computational Economics, vol. 55(4), pages 1275-1299, April.
    2. Andreou, Elena & Werker, Bas J.M., 2015. "Residual-based rank specification tests for AR–GARCH type models," Journal of Econometrics, Elsevier, vol. 185(2), pages 305-331.
    3. Chuffart, Thomas & Hooper, Emma, 2019. "An investigation of oil prices impact on sovereign credit default swaps in Russia and Venezuela," Energy Economics, Elsevier, vol. 80(C), pages 904-916.
    4. Houda Rharrabti Zaid, 2015. "Transmission du stress financier de la zone euro aux Pays de l’Europe Centrale et Orientale," EconomiX Working Papers 2015-37, University of Paris Nanterre, EconomiX.
    5. Khayat, Guillaume A., 2018. "The impact of setting negative policy rates on banking flows and exchange rates," Economic Modelling, Elsevier, vol. 68(C), pages 1-10.
    6. Maddalena Cavicchioli, 2015. "Likelihood Ratio Test and Information Criteria for Markov Switching Var Models: An Application to the Italian Macroeconomy," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 1(3), pages 315-332, November.
    7. Yong Song & Tomasz Wo'zniak, 2020. "Markov Switching," Papers 2002.03598,
    8. Sergei Koulayev & Marc Rysman & Scott Schuh & Joanna Stavins, 2016. "Explaining adoption and use of payment instruments by US consumers," RAND Journal of Economics, RAND Corporation, vol. 47(2), pages 293-325, May.
    9. 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.
    10. Girardin, Eric & Salimi Namin, Fatemeh, 2019. "The January effect in the foreign exchange market: Evidence for seasonal equity carry trades," Economic Modelling, Elsevier, vol. 81(C), pages 422-439.
    11. Andrea Beccarini, 2019. "Testing for the omission of relevant variables and regime-switching misspecification," Empirical Economics, Springer, vol. 56(3), pages 775-796, March.
    12. Gustavo Cabrera González, 2019. "Modeling and Projection of the Mexican Exchange Rate (Peso/Dollar): a Bayesian Approach for Model Selection," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 14(2), pages 203-219, Abril-Jun.
    13. 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.
    14. Abhimanyu Gupta & Myung Hwan Seo, 2019. "Structural stability of infinite-order regression," Papers 1911.08637,
    15. Christian Friedrich & Pierre Guérin, 2020. "The Dynamics of Capital Flow Episodes," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 52(5), pages 969-1003, August.
    16. Luke Hartigan, 2015. "Changes in the Factor Structure of the U.S. Economy: Permanent Breaks or Business Cycle Regimes?," Discussion Papers 2015-17, School of Economics, The University of New South Wales.
    17. Timo Teräsvirta, 2017. "Nonlinear models in macroeconometrics," CREATES Research Papers 2017-32, Department of Economics and Business Economics, Aarhus University.
    18. Anwar Khayat, 2015. "Negative Policy Rates, Banking Flows and Exchange Rates," Working Papers halshs-01203609, HAL.
    19. 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.
    20. Horváth, Lajos & Trapani, Lorenzo, 2019. "Testing for randomness in a random coefficient autoregression model," Journal of Econometrics, Elsevier, vol. 209(2), pages 338-352.
    21. Anwar Khayat, 2015. "Negative Policy Rates, Banking Flows and Exchange Rates," AMSE Working Papers 1538, Aix-Marseille School of Economics, France, revised Sep 2015.
    22. Herrera, Ana María & Hu, Liang & Pastor, Daniel, 2018. "Forecasting crude oil price volatility," International Journal of Forecasting, Elsevier, vol. 34(4), pages 622-635.
    23. James Morley, 2019. "The business cycle: periodic pandemic or rollercoaster ride?," International Journal of Economic Policy Studies, Springer, vol. 13(2), pages 425-431, August.
    24. Thomas Walther & Lanouar Charfeddine & Tony Klein, 2018. "Oil Price Changes and U.S. Real GDP Growth: Is this Time Different?," Working Papers on Finance 1816, University of St. Gallen, School of Finance.

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