Quantile Forecasts
Asymmetric costs have an asymmetric answer. If being short costs three times as much as being long, the target is not the mean.
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Point Forecasts
A point forecast is one summary of a distribution. Reporting only the summary discards the part a decision usually needs.
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Normal Distribution
Most forecast intervals assume normality, and the assumption is least reliable exactly in the tails — which is where risk questions live.
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Probabilistic Forecasts
A point forecast is one summary of this. Once you keep the whole distribution, the decision can pick the summary it actually needs.
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Deterministic forecasts
Reported without an interval, a forecast carries no way of telling how accurate it is — which is why a single line reads as certainty.
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Prediction Intervals (PI)
Interval width depends on the model and horizon. Coverage reflects the uncertainty represented in the model, not every possible change in the world.
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Quantile Regression
Swap squared error for an asymmetric loss and the fitted line becomes a quantile. Three fits give you an interval with no normality assumption.