On Figure 4.18: System activity diagram when making a prediction,

It shows that you sample from the MCMs. How do you sample that 10,000 times if there's just a few months worth of data. I was a little confused on that part. I'm under the impression that you're trying to get the steady state vector by raising the transition matrix to the 10000th power (you could also use system of equations to solve for it).

Markov probabilities have a steady state matrix where the first value is p and the second is 1 -p (p is probability of occurring). So if you solve by a system of equations and get those probabilities (the v in vP^m = v and m is the power), do you then multiply that value by the weighted average in the Prediction Evaluator?

Also how does confidence interval formula play a part with the markov? I keep thinking you just multiply the markov probability by the best fit weighted average mean to make a prediction. Is that a correct assumption?