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A likelihood ratio test for stationarity of rating transitions

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  • Weißbach, Rafael
  • Walter, Ronja

Abstract

We study the time-stationarity of rating transitions, modelled by a time-continuous discrete-state Markov process and derive a likelihood ratio test. For multiple Markov processes from a multiplicative intensity model, maximum likelihood parameter estimates can be written as martingale transform of the processes, counting transitions between the rating states, so that the profile partial likelihood ratio is asymptotically [chi]2-distributed. An application to an internal rating data set reveals highly significant instationarity.

Suggested Citation

  • Weißbach, Rafael & Walter, Ronja, 2010. "A likelihood ratio test for stationarity of rating transitions," Journal of Econometrics, Elsevier, vol. 155(2), pages 188-194, April.
    • Handle: RePEc:eee:econom:v:155:y:2010:i:2:p:188-194
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    References listed on IDEAS

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    1. Kleff Volker & Weber Martin, 2008. "How Do Banks Determine Capital? Evidence from Germany," German Economic Review, De Gruyter, vol. 9(3), pages 354-372, August.
    2. Rafael Weißbach & Patrick Tschiersch & Claudia Lawrenz, 2009. "Testing time-homogeneity of rating transitions after origination of debt," Empirical Economics, Springer, vol. 36(3), pages 575-596, June.
    3. Koopman, Siem Jan & Lucas, Andre & Monteiro, Andre, 2008. "The multi-state latent factor intensity model for credit rating transitions," Journal of Econometrics, Elsevier, vol. 142(1), pages 399-424, January.
    4. Kiefer, Nicholas M., 1985. "Specification diagnostics based on Laguerre alternatives for econometric models of duration," Journal of Econometrics, Elsevier, vol. 28(1), pages 135-154, April.
    5. repec:bla:germec:v:9:y:2008:i::p:354-372 is not listed on IDEAS
    6. Heckman, James J. & Singer, Burton, 1984. "Econometric duration analysis," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 63-132.
    7. Lando, David & Skodeberg, Torben M., 2002. "Analyzing rating transitions and rating drift with continuous observations," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 423-444, March.
    8. Kiefer, Nicholas M. & Larson, C. Erik, 2007. "A simulation estimator for testing the time homogeneity of credit rating transitions," Journal of Empirical Finance, Elsevier, vol. 14(5), pages 818-835, December.
    9. Christensen, Jens H.E. & Hansen, Ernst & Lando, David, 2004. "Confidence sets for continuous-time rating transition probabilities," Journal of Banking & Finance, Elsevier, vol. 28(11), pages 2575-2602, November.
    10. Bangia, Anil & Diebold, Francis X. & Kronimus, Andre & Schagen, Christian & Schuermann, Til, 2002. "Ratings migration and the business cycle, with application to credit portfolio stress testing," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 445-474, March.
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    Citations

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    Cited by:

    1. Rafael Weißbach & Lucas Radloff, 2020. "Consistency for the negative binomial regression with fixed covariate," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(5), pages 627-641, July.
    2. Voß, Sebastian & Weißbach, Rafael, 2014. "A score-test on measurement errors in rating transition times," Journal of Econometrics, Elsevier, vol. 180(1), pages 16-29.
    3. Weißbach, Rafael & Mollenhauer, Thomas, 2011. "Modelling Rating Transitions," VfS Annual Conference 2011 (Frankfurt, Main): The Order of the World Economy - Lessons from the Crisis 48698, Verein für Socialpolitik / German Economic Association.
    4. Alexander Kremer & Rafael Weißbach, 2013. "Consistent estimation for discretely observed Markov jump processes with an absorbing state," Statistical Papers, Springer, vol. 54(4), pages 993-1007, November.
    5. Benjamin Strohner & Rafael Weißbach, 2016. "Altersspezifische Querschnittsanalyse der Fertilität in Mecklenburg-Vorpommern mit dem EM-Algorithmus [Age-Specific Cross-Sectional Analysis of the Fertility in Mecklenburg-West Pomerania with the EM Algorithm]," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 10(4), pages 269-288, December.
    6. Rafael Weißbach & Yongdai Kim & Achim Dörre & Anne Fink & Gabriele Doblhammer, 2021. "Left-censored dementia incidences in estimating cohort effects," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(1), pages 38-63, January.
    7. Rafael Weißbach & Wladislaw Poniatowski & Walter Krämer, 2013. "Nearest neighbor hazard estimation with left-truncated duration data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(1), pages 33-47, January.
    8. Rafael Weißbach & Dominik Wied, 2022. "Truncating the exponential with a uniform distribution," Statistical Papers, Springer, vol. 63(4), pages 1247-1270, August.
    9. Rafael Weißbach & Achim Dörre & Dominik Wied & Gabriele Doblhammer & Anne Fink, 2024. "Left-truncated health insurance claims data: theoretical review and empirical application," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(1), pages 31-68, March.
    10. Weißbach, Rafael & Strohecker, Fynn, 2016. "Modeling rating transitions with instantaneous default," Economics Letters, Elsevier, vol. 145(C), pages 38-40.

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