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I was reading a chapter on prediction intervals and saw that the standard deviation is used to calculate "prediction" intervals. Earlier today I was reading some results from GEFCom2017 where forecasters were required to submit "quantile" intervals not prediction intervals.

  1. How are these quantile intervals calculated?

  2. Also, I have seen some people generate prediction intervals by forecasting the outcome and forecasting the standard deviation of the outcome then generating prediction intervals with those values. Is it possible to do something similar with quantiles?

  3. If one wanted to produce a benchmark with a seasonal naive forecast how would quantile forecast benchmarks be calculated from it.

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Quantile forecasts are really little different from prediction intervals. For instance, if you want a symmetric 90% prediction interval, you would use the interval between a 5% and a 95% quantile forecast. (As a matter of fact, I don't really see a way of calculating prediction intervals that does not explicitly or implicitly use two quantile forecasts.)

That said:

  1. Each submission to the Global Energy Forecasting Competition 2017 (GEFCom2017) of course used a different approach to calculating these quantile forecasts. Many of the submissions were explained in papers that appeared in a special issue of the International Journal of Forecasting, somewhat confusingly entitled "Energy Forecasting In The Big Data World". It's volume 35, issue 4 of the IJF, and the various papers make for interesting reading.

  2. Yes, that ties into my opening paragraph: if you have an expectation forecast and a forecast of the future standard deviation, you can add a distributional assumption (e.g., normal) to the mix and derive predicted quantiles, and any two quantiles will give you a prediction interval.

  3. Energy data typically has rather long histories, with many observed seasonal cycles.

    Energy demand usually exhibits , so when we talk about a "seasonal naive forecast", we need to specify which seasonal cycle we are talking about. The simplest and highest frequency one is the intra-daily cycle. There are also intra-weekly and intra-yearly cycles.

    So if the seasonality is the intra-daily one, then we can derive a "seasonal naive 90% quantile forecast" for next Monday by taking the observations from all past Mondays and taking the empirical 90% quantile of these - interpolating when necessary.

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