I've been given a dataset with a number of observable states. I am trying to apply a Finite State Markov Chain to model the system, but I found that I can't estimate the transition probabilities if the observed states were sampled using different time intervals. How can I find these probabilities?
I will try to make the question a more clear. I have samples collected in random intervals during a 6-month period. This samples represent the "quality" of a system, which is ranked from 0 to 15 in discrete intervals i.e. (0,1,2...15). I need to model de system using a FSMC to mimic the system's behavior. So far, I have estimated the transition probabilities between states using only the frequencies of those transitions using all the samples. I am not interested in modeling the time, however, I am not sure If I can estimate the transition probabilities in such a simple way or if I have to take the time between samples (which in my case is random) into consideration when estimating those probabilities.