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Say you have in your hand a transition matrix published by Moody, and you also collected the rating information for a sample of bonds, which you use to form your own transition matrix. How can we use our sample to test whether if Moody's transition matrix is correct?

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testing with only one sample is somewhat questionable. How much data do you have ? – Probilitator Mar 11 '14 at 16:31
About 1000 bonds – Sam Li Mar 11 '14 at 23:23
up vote 2 down vote accepted

Depending upon how much data you have, you might find Violi (2004) useful.

Nickell et al. (2000), while principally considering time-dependent stability tests, refers a bit to significance testing between the matrices of different agencies and might also provide some insight.

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