I have a multivariate dataset, say M x N, where M is the number of variables and N is the number of samples. Now, the pattern of dependencies between the M variables changes across the N samples i.e. the pattern of dependencies is non-stationary.
I want to use a 'discrete' Markov Model to characterize this change in pattern of dependencies across samples. One way of doing this is by estimating the pattern of dependencies for each sample and using for e.g. k-means clustering to group these patterns into a small number of symbols. Then, I could use Markov Modelling to estimate transition probabilities between symbols.
My question is: can I do all the above in a single unified model i.e. a model which combines the Markov Modelling with estimating patterns of dependencies and clustering them into a small number of symbols. If so, wouldn't this be preferable to the sequential approach outlined above?
Any suggestions/thoughts/ideas welcome!