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thanks for the help in my previous post which describes my issue.

I fitted a seasonal ARIMA model to my daily temperature time series. My goal is to run the forecast lets say 10,000 times in order to get differing forecasted values, like e.g. with geometric brownian motiongeometric brownian motion

Unfortunately ARIMA is deterministic and thus I receive the same output. In the end I want to have 10,000 values at each point in future time. I want to use these values to calculate a density function.

  1. Can bootstrapping solve this problem?
  2. Any other way to obtain differing values with forecast?
  3. Is there a way to extract values from the prediction intervals?
Richard Hardy
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user163494
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  • Related posts by the same user on the topic: [1](https://stats.stackexchange.com/questions/286725/arima-stochastic-component) and [2](https://stats.stackexchange.com/questions/286731/get-random-trials-distribution-from-seasonal-arima-forecast). – Richard Hardy Jun 23 '17 at 10:51
  • You do get a density forecast from ARIMA by default. There is a point forecast, but there is a density forecast as well. It is based on the error distribution (which most often is assumed to be Normal and only its variance is estimated). – Richard Hardy Jun 23 '17 at 11:12
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    No Arima is not deterministic, Arima is a stochastic forecasting technique. – forecaster Jun 23 '17 at 11:16
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    @forecaster, right, just as I explained in the comments to OPs other posts linked in my previous comment above... – Richard Hardy Jun 23 '17 at 11:17
  • Okay, but is there any possibility to extract the values from the density forecast? All I need is a set of predicted temperature values. – user163494 Jun 23 '17 at 12:45
  • Or if the error term is assumed to be Normal, how can I obtain the estimated variance? Because, once I know the variance I can simply genrate a normally distributed variable with mean=point estimate and the variance. Or am I wrong? – user163494 Jun 23 '17 at 12:53

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