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Let's say you are given a time series prediction, and it's corresponding 95% upper and lower confidence interval. What would be the best metric for summarizing these confidence intervals in a single, easy-to-understand number?

I.E. Maybe you could take the width of the confidence interval as a percentage of the prediction?

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Your suggestion is on the right track. The margin of error (MOE) is usually defined as the half-width of the interval, which is expressed either in absolute units or as a percentage of the prediction. For example, you could write, "The predicted value is $12 \pm 3$ or $12 \pm 25$% with 95% confidence."

Note that the term confidence interval applies to the uncertainty in model parameter estimates whereas a prediction interval is for expressing the uncertainty in a prediction.

Also keep in mind the concept of coverage probability, which is the probability, under repeated sampling, that the prediction interval will contain the true value. If the assumptions of your model align well with the data generating process (i.e. the underlying phenomenon) - for example, your model assumes normally-distributed errors and the errors truly are normally-distributed - then the confidence level will be about equal to the coverage probability. If not, a presumed 95% prediction interval could in fact be only a 70 or 80% prediction interval. This article explains the concept further.

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