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I want to fit a (S)ARIMA model to a temperature time series and use it for a forecast afterwards. It is crucial to get a distribution of the predicted values at a time and thus, there must be a random factor included.

Bootstraping might be a solution, but I don't know if that is applicable with the seasonal component and how to do it in R. Any idea?

Or any other idea how to get different forecasted values?

Richard Hardy
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user163494
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  • You actually get a distribution from the standard (S)ARIMA model without bootstrapping. The error distribution is estimated during fitting and forecasted accordingly. Forecast intervals are often displayed by default in statistical software. They are based on forecasted distributions. – Richard Hardy Jun 22 '17 at 13:57
  • Thanks again Richard Hardy! So basically all I need to do is predict the temperature via the model many times? – user163494 Jun 22 '17 at 14:41
  • One time is enough if you need a density forecast rather than just a point forecast. But you can improve the density forecast by including the effect of parameter uncertainty extra to the estimated error density, and this can be done by bootstrapping. See Rob J. Hyndman's work on bagging ETS forecasts (conceptually ETS is not that far away from ARIMA). – Richard Hardy Jun 22 '17 at 15:06
  • Okay, I'd rather stick to SARIMA. But do I end up having lets say 10000 values if the forecast is conducted 10000 times? – user163494 Jun 22 '17 at 17:04
  • Thank you Richard Hardy. Any way to extract the values from the distribution at a given point in future time? – user163494 Jun 23 '17 at 10:52
  • You can generate a random sample from a given distribution. (E.g. rnorm(n) generates an $n$-long sample of N(0,1) variables.) But the forecasted distribution is more informative than just some values sampled from it, so why bother. – Richard Hardy Jun 23 '17 at 10:55

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