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How can i evaluate probabilistic forecast results?

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How can i evaluate prediction interval or density forecast result like reliabilty, skill or sharpness? Few papers i read used prediction interval coverage probability (PICP) and the mean prediction interval width (MPIW) can be used for prediction interval or CRPS but i am not sure how to interpret the results, since i am trying to use point forecast's error distribution. Thanks
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Adam Danz
Adam Danz on 27 Aug 2021
Edited: Adam Danz on 27 Aug 2021
C(i) is 1 when yi in the interval [Li, Ui] and 0 if it's not in that interval.

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