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Rate of Occurrence of Failures (ROCOF) of Higher-Order for Markov Processes: Analysis, Inference and Application to Financial Credit Ratings

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  • Guglielmo D’Amico

    (Università G. d’Annunzio)

Abstract

In this paper we consider the problem of defining rate of occurrence of failures of higher orders for a system whose states form a finite state Markov jump process. Firstly, we derive an explicit formula for evaluating the rate of occurrence of failures of higher order for the system. Secondly, we propose a nonparametric statistical estimator of this function and we discuss its asymptotic properties. The covariance matrix and the asymptotic variance are computed by using the technology of multidimensional matrices. Finally, we provide applications to the modeling of financial credit ratings.

Suggested Citation

  • Guglielmo D’Amico, 2015. "Rate of Occurrence of Failures (ROCOF) of Higher-Order for Markov Processes: Analysis, Inference and Application to Financial Credit Ratings," Methodology and Computing in Applied Probability, Springer, vol. 17(4), pages 929-949, December.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:4:d:10.1007_s11009-015-9437-8
    DOI: 10.1007/s11009-015-9437-8
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    References listed on IDEAS

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    1. Ouhbi, Brahim & Limnios, Nikolaos, 2002. "The rate of occurrence of failures for semi-Markov processes and estimation," Statistics & Probability Letters, Elsevier, vol. 59(3), pages 245-255, October.
    2. 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.
    3. Valérie Girardin & André Sesboüé, 2009. "Comparative Construction of Plug-in Estimators of the Entropy Rate of Two-state Markov Chains," Methodology and Computing in Applied Probability, Springer, vol. 11(2), pages 181-200, June.
    4. 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.
    5. Amparo Baíllo & José Luis Fernández, 2007. "A simple Markov chain structure for the evolution of credit ratings," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 23(6), pages 483-492, November.
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