A likelihood ratio test for stationarity of rating transitions

For a time-continuous discrete-state Markov process as model for rating transitions, we study the time-stationarity by means of a likelihood ratio test. For multiple Markov process data from a multiplicative intensity model, maximum likelihood parameter estimates can be represented as martingale transform of the processes counting transitions between the rating states. As a consequence, the profile partial likelihood ratio is asymptotically X-2-distributed. An internal rating data set reveals highly significant instationarity.