Statistical Papers

, Volume 54, Issue 4, pp 993–1007 | Cite as

Consistent estimation for discretely observed Markov jump processes with an absorbing state

Regular Article

Abstract

For a continuous-time Markov process, commonly, only discrete-time observations are available. We analyze multiple observations of a homogeneous Markov jump process with an absorbing state. We establish consistency of the maximum likelihood estimator, as the number of Markov processes increases. To accomplish uniform convergence in the continuous mapping theorem, we use the continuity of the transition probability in the parameters, the compactness of the parameter space and the boundedness of probabilities. We allow for a stochastic time-grid of observation points with different intensities for each observation process. Furthermore, we account for right censoring. The estimate is obtained via the EM algorithm with an E-step given in closed form. In our empirical application of credit rating histories, we fit the model of Weißbach and Mollenhauer (J Korean Stat Soc 40:469–485, 2011) and find marked differences, compared to the continuous-time analysis.

Keywords

Multiple markov jump process Credit rating Discrete observations EM Parametric maximum likelihood 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Faculty of Economic and Social SciencesInstitute for Economics, University of RostockRostockGermany

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