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Markov Regime-Switching Tests: Asymptotic Critical Values

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  • Steigerwald, Douglas
  • Carter, Andrew

Abstract

Empirical research with Markov regime-switching models often requires the researcher not only to estimate the model but also to test for the presence of more than one regime. Despite the need for both estimation and testing, methods of estimation are better understood than are methods of testing. We bridge this gap by explaining, in detail, how to apply the newest results in the theory of regime testing, developed by Cho and White [Cho, J. S., and H. White 2007. “Testing for Regime Switching.” Econometrica 75 (6): 1671–1720.]. A key insight in Cho and White is to expand the null region to guard against false rejection of the null hypothesis due to a small group of extremal values. Because the resulting asymptotic null distribution is a function of a Gaussian process, the critical values are not obtained from a closed-form distribution such as the χ². Moreover, the critical values depend on the covariance of the Gaussian process and so depend both on the specification of the model and the specification of the parameter space. To ease the task of calculating critical values, we describe the limit theory and detail how the covariance of the Gaussian process is linked to the specification of both the model and the parameter space. Further, we show that for linear models with Gaussian errors, the relevant parameter space governs a standardized index of regime separation, so one need only refer to the tabulated critical values we present. While the test statistic under study is designed to detect regime switching in the intercept, the test can be used to detect broader alternatives in which slope coefficients and error variances may also switch over regimes.
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Suggested Citation

  • Steigerwald, Douglas & Carter, Andrew, 2011. "Markov Regime-Switching Tests: Asymptotic Critical Values," University of California at Santa Barbara, Economics Working Paper Series qt5rn986z6, Department of Economics, UC Santa Barbara.
  • Handle: RePEc:cdl:ucsbec:qt5rn986z6
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    References listed on IDEAS

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    1. Jin Seo Cho & Halbert White, 2007. "Testing for Regime Switching," Econometrica, Econometric Society, vol. 75(6), pages 1671-1720, November.
    2. Andrew V. Carter & Douglas G. Steigerwald, 2012. "Testing for Regime Switching: A Comment," Econometrica, Econometric Society, vol. 80(4), pages 1809-1812, July.
    3. Cecchetti, Stephen G & Lam, Pok-sang & Mark, Nelson C, 1990. "Mean Reversion in Equilibrium Asset Prices," American Economic Review, American Economic Association, vol. 80(3), pages 398-418, June.
    4. Carter Andrew V. & Steigerwald Douglas G., 2013. "Markov Regime-Switching Tests: Asymptotic Critical Values," Journal of Econometric Methods, De Gruyter, vol. 2(1), pages 25-34, July.
    5. 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.
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    Cited by:

    1. Jean-Marie DUFOUR & Richard LUGER, 2016. "Identification-Robust Moment-Based Tests for Markov-Switching in Autoregressive Models," Cahiers de recherche 15-2016, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. James D. Hamilton, 2016. "Macroeconomic Regimes and Regime Shifts," NBER Working Papers 21863, National Bureau of Economic Research, Inc.
    3. Blommestein, Hans & Eijffinger, Sylvester & Qian, Zongxin, 2016. "Regime-dependent determinants of Euro area sovereign CDS spreads," Journal of Financial Stability, Elsevier, vol. 22(C), pages 10-21.
    4. Blommestein, Hans J. & Eijffinger, Sylvester C W & Qian, Zongxin, 2012. "Animal Spirits in the Euro Area Sovereign CDS Market," CEPR Discussion Papers 9092, C.E.P.R. Discussion Papers.
    5. Carter Andrew V. & Steigerwald Douglas G., 2013. "Markov Regime-Switching Tests: Asymptotic Critical Values," Journal of Econometric Methods, De Gruyter, vol. 2(1), pages 25-34, July.
    6. repec:eee:macchp:v2-163 is not listed on IDEAS
    7. Kuhanathan Ano Sujithan & Sanvi Avouyi-Dovi, 2013. "The links between some European financial factors and the BRICS credit default swap spreads," Post-Print hal-01511898, HAL.
    8. Seth J. Kopchak, 2016. "The regime-switching risk premium in the gold futures market," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 40(3), pages 472-491, July.
    9. repec:dau:papers:123456789/11721 is not listed on IDEAS

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    Keywords

    Social and Behavioral Sciences; mixture model; regime switching; numeric approximation;

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