My question relates to probabilistic forecasting. How does one actually go about computing a forecast?
Lets say I have some data that can be modelled by a specific distribution, and the values of the coefficients etc. are known. Therefore, I know the mean of this distribution gives me the expected value, but is this value the forecast? How would the forecast progress?
For example, with ARMA forecasts, the forecasted values are computed using a recursive formula which is updated at each time step with the new value. I don't see how this applies to a probabilistic forecast.
Is it perhaps random (the term might be stochastic)? As in, for each time you want to forecast, you randomly generate a value from the distribution?