Regular Article

Statistical Papers

, Volume 54, Issue 4, pp 993-1007

First online:

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

  • Alexander KremerAffiliated withFaculty of Economic and Social Sciences, Institute for Economics, University of Rostock
  • , Rafael WeißbachAffiliated withFaculty of Economic and Social Sciences, Institute for Economics, University of Rostock Email author 

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

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