I am dealing with following problem.
I have $n=10$ weather stations and for each station I have information about wind direction: a discrete variable with 4 states $\{s, n, w, e\}$.
If I need generate wind direction scenarios for one station I am using a first order Markov chain. But now I need to generate scenarios for all weather stations and i need to include correlation between wind directions for each stations.
Any idea how to model this situation?