We propose the factorial hidden Markov duration (FHMD) process for modeling the dynamics
governing financial price durations. We derive its statistical properties and apply the exact
maximum likelihood (ML) approach to estimate its parameters. The applicability of the
exact ML method, however, becomes computationally infeasible for a large number of latent
factorial components. By employing a simulation-based approximate ML (AML) approach,
we provide a fast and robust alternative estimation procedure, which is not restricted by the
number of factorial components. We show that the AML method provides accurate parameter
estimates in a Monte Carlo study and analyse both estimation routines in an empirical study
using price durations of IBM. The extension of the number of components facilitated by
the AML technique allows us to examine the entire spectrum of model specifications, which
leads to substantial differences in the estimation results and also improves the forecasting
performance.