I have two weakly correlated variables (r2=0.66). I want to include these in a hidden markov model (HMM) alongside other uncorrelated variables. I cannot find anything in the assumptions of HMM's specifying if observable variables can or cannot be correlated. It would make sense to me if some degree of correlation is tolerated but it would be great if someone could answer if this is correct (in simple terms!) or direct me to appropriate reading.
Thanks!
From a modelling perspective, there's no issue with having correlated observables in a HMM. The HMM simply models your data as having a hidden Markov process which projects on to an observed state space. Having correlation in observables means that certain regions of the observed space are extremely unlikely.
The model just learns the emission probabilities from each hidden state to each of your observables. It would actually be sort of weird for your observables to completely uncorrelated given that your modelling them as arising from the same hidden state.
