Please also have a look at the page about stochastic resonance on Azimuth (there are links to review papers in the reference section of that page).
While stochastic resonance has been "invented" to explain the glacial cycles, there are a lot of other systems that exhibit this phenomenon. As an exercise in parametric estimation, you could try to estimate the model parameters of a bistable symmetric potential to temperature series of Earth's history.
It is also quite customary to model stochastic resonance both in continuous time and space and as a discrete system (with discrete time or as a discrete two state Markov system in continuous or discrete time). So this is a natural playing ground for comparing both approaches.
In the case of the glacial cycles there are several periodic or quasi periodic external forcings like the Milankovich cycles, which are most naturally modelled in continuous time. In simulations you'll always use a discrete approximation, of course, so a continuous time model should in this context be viewed as a means to change the time step in your approximation according to your needs, which is a kind of modelling freedom that a discrete Markov model does not have. The continuous time model allows you to compare results obtained for different discretizations, while you have to build in the discretization into a discrete Markov model a priori without any chance to check if that is a good approximation.