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

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...

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Bibliographic Details
Published inStatistical papers (Berlin, Germany) Vol. 54; no. 4; pp. 993 - 1007
Main Authors Kremer, Alexander, Weißbach, Rafael
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2013
Springer Nature B.V
Subjects
Absorption
Algorithms
Consistency
Continuity
Convergence
Credit ratings
Credit risk
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Estimating techniques
Exact solutions
Finance
Insurance
Management
Markov analysis
Markov processes
Mathematical analysis
Mathematical models
Mathematics and Statistics
Monte Carlo simulation
Operations Research/Decision Theory
Probability
Probability Theory and Stochastic Processes
Random variables
Regular Article
Statistical analysis
Statistics
Statistics for Business
Studies
EM
Parametric maximum likelihood
Discrete observations
Multiple markov jump process
Credit rating
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Summary: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.
Bibliography:ObjectType-Article-1
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ISSN:0932-5026
1613-9798
DOI:10.1007/s00362-013-0515-0