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Statistical inference for Markov chains with applications to credit risk

Author

Listed:
  • Linda Möstel

    (Institute for Statistics and Econometrics)

  • Marius Pfeuffer

    (Institute for Statistics and Econometrics)

  • Matthias Fischer

    (Institute for Statistics and Econometrics)

Abstract

The focus of this paper is on the derivation of confidence and credibility intervals for Markov chains when discrete-time, continuous-time or discretely observed continuous-time data are available. Thereby, our contribution is threefold: First, we discuss and compare multinomial confidence regions for the rows of discrete-time Markov transition matrices in the light of empirical characteristics of credit rating migrations. Second, we derive an analytical expression for the expected Fisher information matrix of a continuous-time Markov chain which is used to construct credibility intervals using a non-informative Jeffreys prior distribution and a Metropolis-Hastings Algorithm. Third, we concretize profile and estimated/pseudo likelihood based confidence intervals in the continuous-time data settings, which in contrast to asymptotic normality based intervals explicitly consider non-negativity constraints for the parameters. Furthermore, we illustrate the described methods by Moody’s corporate ratings data with exact continuous-time transitions.

Suggested Citation

  • Linda Möstel & Marius Pfeuffer & Matthias Fischer, 2020. "Statistical inference for Markov chains with applications to credit risk," Computational Statistics, Springer, vol. 35(4), pages 1659-1684, December.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:4:d:10.1007_s00180-020-00978-0
    DOI: 10.1007/s00180-020-00978-0
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    References listed on IDEAS

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    Cited by:

    1. Lapshin, Viktor & Anton, Markov, 2022. "MCMC-based credit rating aggregation algorithm to tackle data insufficiency," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 68, pages 50-72.
    2. Abhik Ghosh, 2022. "Robust parametric inference for finite Markov chains," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 118-147, March.

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