Statistical inference for Markov chains with applications to credit risk

Linda Möstel, Marius Pfeuffer () and Matthias Fischer
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Linda Möstel: Institute for Statistics and Econometrics
Marius Pfeuffer: Institute for Statistics and Econometrics
Matthias Fischer: Institute for Statistics and Econometrics

Computational Statistics, 2020, vol. 35, issue 4, No 7, 1659-1684

Abstract: 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.

Keywords: Transition matrix; Generator matrix; Bootstrap; Jeffreys prior; Metropolis-Hastings algorithm (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00180-020-00978-0

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