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Testing for Uncorrelated Residuals in Dynamic Count Models with an Application to Corporate Bankruptcy

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  • Sant'Anna, Pedro H. C.

Abstract

This article proposes a new diagnostic test for dynamic count models, which is well suited for risk management. Our test proposal is of the Portmanteau-type test for lack of residual autocorrelation. Unlike previous proposals, the resulting test statistic is asymptotically pivotal when innovations are uncorrelated, but not necessarily iid nor a martingale difference. Moreover, the proposed test is able to detect local alternatives converging to the null at the parametric rate T^{1/2}, with T the sample size.The finite sample performance of the test statistic is examined by means of a Monte Carlo experiment. Finally, using a dataset on U.S. corporate bankruptcies, we apply our test proposal to check if common risk models are correctly specified.

Suggested Citation

  • Sant'Anna, Pedro H. C., 2013. "Testing for Uncorrelated Residuals in Dynamic Count Models with an Application to Corporate Bankruptcy," MPRA Paper 48376, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:48376
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    References listed on IDEAS

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    1. Siem Jan Koopman & André Lucas & Bernd Schwaab, 2012. "Dynamic Factor Models With Macro, Frailty, and Industry Effects for U.S. Default Counts: The Credit Crisis of 2008," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 521-532, May.
    2. Darrell Duffie & Andreas Eckner & Guillaume Horel & Leandro Saita, 2009. "Frailty Correlated Default," Journal of Finance, American Finance Association, vol. 64(5), pages 2089-2123, October.
    3. Benjamin M.A. & Rigby R.A. & Stasinopoulos D.M., 2003. "Generalized Autoregressive Moving Average Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 214-223, January.
    4. Escanciano, J. Carlos & Lobato, Ignacio N., 2009. "An automatic Portmanteau test for serial correlation," Journal of Econometrics, Elsevier, vol. 151(2), pages 140-149, August.
    5. Robert C. Jung & A. R. Tremayne, 2003. "Testing for serial dependence in time series models of counts," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 65-84, January.
    6. Hong, Yongmiao, 1996. "Consistent Testing for Serial Correlation of Unknown Form," Econometrica, Econometric Society, vol. 64(4), pages 837-864, July.
    7. Richard A. Davis, 2003. "Observation-driven models for Poisson counts," Biometrika, Biometrika Trust, vol. 90(4), pages 777-790, December.
    8. Delgado, Miguel A. & Velasco, Carlos, 2011. "An Asymptotically Pivotal Transform of the Residuals Sample Autocorrelations With Application to Model Checking," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 946-958.
    9. Lobato, I.N. & Nankervis, John C. & Savin, N.E., 2002. "Testing For Zero Autocorrelation In The Presence Of Statistical Dependence," Econometric Theory, Cambridge University Press, vol. 18(03), pages 730-743, June.
    10. Francq, Christian & Roy, Roch & Zakoian, Jean-Michel, 2005. "Diagnostic Checking in ARMA Models With Uncorrelated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 532-544, June.
    11. 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.
    12. Escanciano, J. Carlos, 2009. "On The Lack Of Power Of Omnibus Specification Tests," Econometric Theory, Cambridge University Press, vol. 25(01), pages 162-194, February.
    13. Fokianos, Konstantinos & Tjøstheim, Dag, 2011. "Log-linear Poisson autoregression," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 563-578, March.
    14. Dag Tjøstheim, 2012. "Some recent theory for autoregressive count time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 413-438, September.
    15. Delgado, Miguel A. & Velasco, Carlos, 2010. "Distribution-free tests for time series models specification," Journal of Econometrics, Elsevier, vol. 155(2), pages 128-137, April.
    16. Koopman, Siem Jan & Lucas, André & Schwaab, Bernd, 2011. "Modeling frailty-correlated defaults using many macroeconomic covariates," Journal of Econometrics, Elsevier, vol. 162(2), pages 312-325, June.
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    More about this item

    Keywords

    Time Series of counts; Residual autocorrelation function; Model checking; Credit risk management.;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • G3 - Financial Economics - - Corporate Finance and Governance
    • G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation

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