Modelling Transition Between States without Markov Property

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I have a data set that I'm trying to model out.

My data set tracks an individual items over 20 periods. In each period each item can be in one of four states. There are no restrictions on how items can move between states.

I want to be able to calculate the probability of movements between states. The movement to the next state is dependent on the time spent in the previous state so I wouldn't be able to use a Markov process. Is there an alternative approach that I can use?

Thanks!

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You can make it into a Markov process if you include time information in the "state".