Probabilistic forecasting methods
A point forecast is shown with the true future values, then an 80% prediction interval is drawn around it and most of the true values fall inside it (10 of 12). Then four panels show how the interval is built: bootstrapping simulates future paths with resampled residuals and takes their quantiles, so the interval can be asymmetric and widen with the horizon; conformal prediction adds and subtracts the 80% quantile of the absolute residuals, a symmetric interval of constant width; quantile regression trains one model per bound, so the interval can be asymmetric and the bounds can cross; and foundation models predict the quantiles directly, without residuals or training.
Probabilistic forecasting methods
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Intervals
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From residuals
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Direct quantiles
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skforecast.org
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