First of all, please excuse if I don't use the proper terminology for this problem.
I have a markov chain composed by two states:
- When in state 1 the output is drawn from an exponential distribution with mean parameter mu_exp
- When in state 2 the output is drawn from a gaussian distribution with mean mu_gaus and standard deviation gamma_gaus
I have a time series which I assume as being ruled by that markov model.
My objective is to generate many random outcomes from that markov model and test its likelihood with the original time series.
Is there a test, like Kolmogorov-Smirnov or mann-whitney-wilcoxon to reject the null-hypotesis "The two series are outcomes of the same markov chain"?
Again, sorry for the terminology, I hope I was clear enough