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Do you know a reference (freely available on the web) where the likelihood ratio test is applied in order to test for the Markov property?

The setting is a directly observable discrete Markov-chain with given transition matrices. The concrete application is a model for credit rating transitions. Some statistical tests are applied in this paper Time series properties of a rating system based on financial ratios but there are too little details.

Evaluating the Markov property by Frank Bickenbach and Eckhardt Bode is an example for testing the Markov property but it is behind a pay wall.

EDIT: The concrete test is: Null hypothesis: rating transitions do not depend on past rating distributions. The alternative hypothesis: rating transitions depend on past rating distributions (in the sense of a 1st order Markov chain).

Richi W
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  • I think a little more context would be helpful, for example, are you working with continuous or discrete variables, is your state space the same as the observed variable... – jbowman Dec 05 '13 at 14:23
  • @ jbowman Yes, sorry. I have edited the question. It is simple discrete setting directly observable. – Richi W Dec 05 '13 at 15:08
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    In such cases, I just ask the author directly for a copy: fbickenbach@ifw.uni-kiel.de – A. Donda Dec 06 '13 at 01:51
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    I don't remember whether they do a likelihood-ratio test, but I think a (the?) classic reference is "Tests for Contingency Tables and Markov Chains", S. Kullback, M. Kupperman and H. H. Ku, Technometrics, Vol. 4, No. 4, (Nov., 1962), pp. 573-608 – unfortunately also pay-only on JSTOR http://www.jstor.org/discover/10.2307/1266291 – A. Donda Dec 06 '13 at 01:52
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    If you don't succeed with the author, I have the paper you mention available, as well as the Kullback et al paper (legally). Let me know. – Alecos Papadopoulos Dec 06 '13 at 20:21
  • What are the null and alternative hypothesis in your test? Null hypothesis seems to be the Markov chain with given transition matrix. Alternative is ...? – ywat Dec 08 '13 at 15:48
  • @ywat very good question: Null hypothesis: rating transitions do not depend on past rating distributions. The alternative hypothesis: rating transitions depend on past rating distributions (in the sense of a 1st order Markov chain). – Richi W Dec 09 '13 at 08:55
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    @AlecosPapadopoulos You have sent the reference - I would like to award the bounty to you. Can you somehow make it an answer? – Richi W Dec 09 '13 at 08:59
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    No, Richard, I cannot accept that. Just _possessing_ a reference that _somebody else proposed_, cannot be considered an answer. If it was I that I have come up with these references as my suggestions to you,then yes, that would be an answer, and so eligible for upvotes, downvotes, bounties, etc. But this is not the case here. People seem to take an interest in your question, and there is a probability of receiving a proper answer. So I would suggest to you to cultivate this interest, and exhaust the deadline and any grace period available, for the bounty. – Alecos Papadopoulos Dec 09 '13 at 14:29

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