An EM algorithm for continuous-time bivariate Markov chains
We study properties and parameter estimation of a finite-state, homogeneous, continuous-time, bivariate Markov chain. Only one of the two processes of the bivariate Markov chain is assumed observable. The general form of the bivariate Markov chain studied here makes no assumptions on the structure of the generator of the chain. Consequently, simultaneous jumps of the observable and underlying processes are possible, neither process is necessarily Markov, and the time between jumps of each of the two processes has a phase-type distribution. Examples of bivariate Markov chains include the Markov modulated Poisson process and the batch Markovian arrival process when appropriate modulo counts are used in each case. We develop an expectation–maximization (EM) procedure for estimating the generator of a bivariate Markov chain, and we demonstrate its performance. The procedure does not rely on any numerical integration or sampling scheme of the continuous-time bivariate Markov chain. The proposed EM algorithm is equally applicable to multivariate Markov chains.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Robert B. Israel & Jeffrey S. Rosenthal & Jason Z. Wei, 2001. "Finding Generators for Markov Chains via Empirical Transition Matrices, with Applications to Credit Ratings," Mathematical Finance, Wiley Blackwell, vol. 11(2), pages 245-265.
- Leroux, Brian G., 1992. "Maximum-likelihood estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 127-143, February.
- Erhan Çinlar, 1975. "Exceptional Paper--Markov Renewal Theory: A Survey," Management Science, INFORMS, vol. 21(7), pages 727-752, March.
When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:504-517. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.