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Testing for Regime Switching: A Comment

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  • Andrew V. Carter
  • Douglas G. Steigerwald

Abstract

In Cho and White (2007) "Testing for Regime Switching" the authors obtain the asymptotic null distribution of a quasi-likelihood ratio (QLR) statistic. The statistic is designed to test the null hypothesis of one regime against the alternative of Markov switching between two regimes. Likelihood ratio statistics are used because the test involves nuisance parameters that are not identified under the null hypothesis, together with other nonstandard features. Cho and White focus on a quasi-likelihood, which ignores certain serial correlation properties but allows for a tractable factorization of the likelihood. While the majority of their paper focuses on asymptotic behavior under the null hypothesis, Theorem 1(b) states that the quasi-maximum likelihood estimator (QMLE) is consistent under the alternative hypothesis. Consistency of the QMLE requires that the expected quasi-log-likelihood attain a global maximum at the population parameter values. This requirement holds for some Markov regime-switching processes but, as we show below, not for an autoregressive process as analyzed in Cho and White.
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Suggested Citation

  • Andrew V. Carter & Douglas G. Steigerwald, 2012. "Testing for Regime Switching: A Comment," Econometrica, Econometric Society, vol. 80(4), pages 1809-1812, July.
    • Handle: RePEc:ecm:emetrp:v:80:y:2012:i:4:p:1809-1812
    DOI: ECTA9622
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    References listed on IDEAS

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    1. Levine, David, 1983. "A remark on serial correlation in maximum likelihood," Journal of Econometrics, Elsevier, vol. 23(3), pages 337-342, December.
    2. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, Decembrie.
    3. Sean D. Campbell, 2002. "Specification Testing and Semiparametric Estimation of Regime Switching Models: An Examination of the US Short Term Interest Rate," Working Papers 2002-26, Brown University, Department of Economics.
    4. Kim, Chang-Jin & Piger, Jeremy & Startz, Richard, 2008. "Estimation of Markov regime-switching regression models with endogenous switching," Journal of Econometrics, Elsevier, vol. 143(2), pages 263-273, April.
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    1. Boris Blagov, 2018. "Financial crises and time-varying risk premia in a small open economy: a Markov-switching DSGE model for Estonia," Empirical Economics, Springer, vol. 54(3), pages 1017-1060, May.
    2. Demian Pouzo & Zacharias Psaradakis & Martin Sola, 2023. "A Note on Quasi-Maximum-Likelihood Estimation in Hidden Markov Models with Covariate-Dependent Transition Probabilities," Working Papers 234, Red Nacional de Investigadores en Economía (RedNIE).
    3. Valerie K. Bostwick & Douglas G. Steigerwald, 2014. "Obtaining critical values for test of Markov regime switching," Stata Journal, StataCorp LP, vol. 14(3), pages 481-498, September.
    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. Boris Blagov & Michael Funke & Richhild Moessner, 2015. "Modelling the time-variation in euro area lending spreads," BIS Working Papers 526, Bank for International Settlements.
    6. Hiroyuki Kasahara & Katsumi Shimotsu, 2018. "Testing the Number of Regimes in Markov Regime Switching Models," Papers 1801.06862, arXiv.org, revised Jan 2018.
    7. 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.
    8. Candelon, Bertrand & Metiu, Norbert & Straetmans, Stefan, 2013. "Disentangling economic recessions and depressions," Discussion Papers 43/2013, Deutsche Bundesbank.
    9. 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.
    10. 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.
    11. Demian Pouzo & Zacharias Psaradakis & Martin Sola, 2022. "Maximum Likelihood Estimation in Markov Regime‐Switching Models With Covariate‐Dependent Transition Probabilities," Econometrica, Econometric Society, vol. 90(4), pages 1681-1710, July.
    12. Pierre Guérin & Danilo Leiva-Leon & Massimiliano Marcellino, 2020. "Markov-Switching Three-Pass Regression Filter," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 285-302, April.
    13. 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.
    14. Pierre Guérin & Danilo Leiva-Leon & Massimiliano Marcellino, 2020. "Markov-Switching Three-Pass Regression Filter," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 285-302, April.

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