# Discrete scenarios from an ARMA forecast

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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As @IrishStat says, you can't associate probability values with specific future sample paths. It is not clear what you mean by "forecast a series" -- you can just string together the point forecasts for different horizons and you get forecasts for the series. Perhaps you want prediction intervals with specified probabilities for future values -- but any software will do that, so I suspect you want something else. Can you provide more information? –  Rob Hyndman Mar 14 '12 at 23:35
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## 1 Answer

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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