IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v57y2011i3p487-505.html
   My bibliography  Save this article

A New Goodness-of-Fit Test for Event Forecasting and Its Application to Credit Defaults

Author

Listed:
  • Andreas Blöchlinger

    () (Zürcher Kantonalbank, 8010 Zurich, Switzerland)

  • Markus Leippold

    () (University of Zurich, 8032 Zurich, Switzerland)

Abstract

We develop a new goodness-of-fit test for validating the performance of probability forecasts. Our test statistic is particularly powerful under sparseness and dependence in the observed data. To build our test statistic, we start from a formal definition of calibrated forecasts, which we operationalize by introducing two components. The first component tests the level of the estimated probabilities; the second validates the shape, measuring the differentiation between high and low probability events. After constructing test statistics for both level and shape, we provide a global goodness-of-fit statistic, which is asymptotically \chi 2 distributed. In a simulation exercise, we find that our approach is correctly sized and more powerful than alternative statistics. In particular, our shape statistic is significantly more powerful than the Kolmogorov-Smirnov test. Under independence, our global test has significantly greater power than the popular Hosmer-Lemeshow's \chi 2 test. Moreover, even under dependence, our global test remains correctly sized and consistent. As a timely and important empirical application of our method, we study the validation of a forecasting model for credit default events. This paper was accepted by Wei Xiong, finance.

Suggested Citation

  • Andreas Blöchlinger & Markus Leippold, 2011. "A New Goodness-of-Fit Test for Event Forecasting and Its Application to Credit Defaults," Management Science, INFORMS, vol. 57(3), pages 487-505, March.
  • Handle: RePEc:inm:ormnsc:v:57:y:2011:i:3:p:487-505
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.1100.1283
    Download Restriction: no

    References listed on IDEAS

    as
    1. Wei Pan, 2002. "Goodness-of-fit Tests for GEE with Correlated Binary Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 101-110.
    2. Donald W. K. Andrews, 2005. "Cross-Section Regression with Common Shocks," Econometrica, Econometric Society, vol. 73(5), pages 1551-1585, September.
    3. Han Bleichrodt & Jose Luis Pinto, 2000. "A Parameter-Free Elicitation of the Probability Weighting Function in Medical Decision Analysis," Management Science, INFORMS, vol. 46(11), pages 1485-1496, November.
    4. G. Noether, 1963. "Note on the kolmogorov statistic in the discrete case," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 7(1), pages 115-116, December.
    5. William Harbaugh & Kate Krause & Lise Vesterlund, 2002. "Risk Attitudes of Children and Adults: Choices Over Small and Large Probability Gains and Losses," Experimental Economics, Springer;Economic Science Association, vol. 5(1), pages 53-84, June.
    6. Gordy, Michael B., 2003. "A risk-factor model foundation for ratings-based bank capital rules," Journal of Financial Intermediation, Elsevier, vol. 12(3), pages 199-232, July.
    7. Orme, Christopher, 1988. "The Calculation of the Information Matrix Test for Binary Data Models," The Manchester School of Economic & Social Studies, University of Manchester, vol. 56(4), pages 370-376, December.
    8. Gordy, Michael B., 2000. "A comparative anatomy of credit risk models," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 119-149, January.
    9. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    10. Sanjiv R. Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2007. "Common Failings: How Corporate Defaults Are Correlated," Journal of Finance, American Finance Association, vol. 62(1), pages 93-117, February.
    11. Archer, Kellie J. & Lemeshow, Stanley & Hosmer, David W., 2007. "Goodness-of-fit tests for logistic regression models when data are collected using a complex sampling design," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4450-4464, May.
    12. Hanson, Samuel & Schuermann, Til, 2006. "Confidence intervals for probabilities of default," Journal of Banking & Finance, Elsevier, vol. 30(8), pages 2281-2301, August.
    13. Cubitt, Robin P & Starmer, Chris & Sugden, Robert, 1998. "Dynamic Choice and the Common Ratio Effect: An Experimental Investigation," Economic Journal, Royal Economic Society, vol. 108(450), pages 1362-1380, September.
    14. Blochlinger, Andreas & Leippold, Markus, 2006. "Economic benefit of powerful credit scoring," Journal of Banking & Finance, Elsevier, vol. 30(3), pages 851-873, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lahiri, Kajal & Wang, J. George, 2013. "Evaluating probability forecasts for GDP declines using alternative methodologies," International Journal of Forecasting, Elsevier, vol. 29(1), pages 175-190.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:57:y:2011:i:3:p:487-505. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc). General contact details of provider: http://edirc.repec.org/data/inforea.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.