A likelihood ratio test for stationarity of rating transitions

We study the time-stationarity of rating transitions, modelled by a time-continuous discrete-state Markov process and derive a likelihood ratio test. For multiple Markov processes from a multiplicative intensity model, maximum likelihood parameter estimates can be written as martingale transform of the processes, counting transitions between the rating states, so that the profile partial likelihood ratio is asymptotically χ2-distributed. An application to an internal rating data set reveals highly significant instationarity.