Given an ARMA model and a historical time series, I'm trying to create a set of $n$ forecast scenarios, where each scenario $s$ is a potential future hourly time series $x_s[t]$, with a given probability, $p_s$. I'm familiar with how to generate an ARMA point forecast for a given horizon - how do you extend this theory to forecast a series?
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Each forecast from an ARIMA model will have 0.0 probability of ocurring since there are infinite number of realizations unlike the roll of a die. You could talk about the probobility of achieving a particular goal/number OR less and this would take on different "probabilities". If for example you were concerned with a probability of obtaining a number or less say 95% then you could simply compute the upper 97.5% value for each period out and call that a sequence of values that are expected to be obtained or less for each point in the forecast period (nf values ). Now simply change your probability and extract the next set of nf values. Hope this helps. In this way you can create a number of realizations where each realization is associated with a probability ( of equal to or less than a specified value ) . |
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