Prediction intervals versus coefficient intervals
Question
Why is uncertainty about a future return usually larger than uncertainty about its conditional mean?
Short answer
A future observation includes irreducible outcome noise in addition to uncertainty about estimated model parameters. An interval for the conditional mean captures estimation uncertainty; a prediction interval must also account for the conditional outcome distribution. Heteroscedasticity, serial dependence and model misspecification complicate both. State the target, horizon and coverage assumptions rather than labelling every uncertainty band a prediction interval.
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Open the worked solutionLessons behind this question
- Ridge, Lasso, and Elastic Net
- The Normal Equations: Closed-Form Least Squares
- Conditional Probability, Total Probability, and Bayes' Rule
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