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...

We propose and illustrate a Markov-switching multi-fractal duration (MSMD) model for analysis of inter-trade durations in financial markets. We establish several of its key properties with emphasis on high persistence (indeed long memory). Empirical exploration suggests MSMD's superiority...