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I am using Hidden Markov Models, having observations as continuous variable and states as discrete variable. I can use the observations to train HMM model and generate n number of states(say 2 hidden states). However, once I am done with the modelling, I know I would be having 2 hidden states and associated parameters of HMM(like initial state probabilities).

However, do we some mechanism to infer the true meaning of those states. Because now I have 2 states S1 and S2, but I don't know what those states represent.

I want to create the states and give true meaning to them. To explain by example, lets assume, I have time series data for Sales and I would like to create 2 hidden states(say Winter/Summer). How do I model this type of hidden states.

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The states that you infer are defined by their emission probabilities. So one of them has a certain probability distribution over the continuous observed variables, and the other one as well. You can try and understand a bit better what they mean by comparing these probability distributions. You will probably not find obvious "true" hidden states, for example, if you model sales, you might find just a repeating pattern of low and high sales, and a low and high state. These would then follow observed high and low sales, but those states could correspond to many things simultaneously, ie. weekends, holidays, summer period, bad weather and so on.

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