I have a univariate time series exhibiting strong periodicity that I want to forecast, and I plan to use ARIMA. However due to specifics of the prediction task that I'm interested in performing, some of the samples are >100x more important than other samples, and I want to make sure that this information is taken into account when I fit the model.

So, is there any way to incorporate the weighting of samples into an ARIMA model?

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    $\begingroup$ In what way are some observations far more important than others? (1) It is far more important to get them right, or (2) these should have a higher weight in predicting subsequent observations? In either case, do you know or do you need to forecast whether the next observation is important? That said, I don't know of such an ARIMA variant, and I'm not sure one could coherently build it. If (1) above, one could try some kind of "time series boosting". $\endgroup$ – Stephan Kolassa Nov 9 '17 at 7:21
  • $\begingroup$ It is far more important to get them right. The cost function I'm minimizing is a function of sums of non-disjoint subsets of predictions, and therefore the number of sums that a given prediction appears in is directly proportional to its contribution to the cost function. $\endgroup$ – jon_simon Nov 14 '17 at 22:55

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