What methodologies can be used to evaluate the uncertainty in time series forecasts?
Instruction: Explain the approaches to quantify and communicate the uncertainty associated with time series forecasts.
Updated
Example Answer
For a future observed value, I would report a prediction distribution or interval, rather than confuse it with a confidence interval for an estimated mean. The interval should include future observation uncertainty under the chosen model. Parameter uncertainty and uncertainty in future inputs may require additional treatment.
Options include model-based simulation, Bayesian posterior prediction, or a bootstrap designed for the dependence structure. Resampling individual observations independently can destroy temporal dependence; block or model-based methods may be more appropriate. I would check empirical coverage by horizon on rolling forecasts and report interval width as well. A nominal ninety-five percent interval can still be badly calibrated after a regime change, so I would communicate its assumptions and scenario limits.
Make it your own
Choose one method and explain which uncertainty it captures and which it leaves out.
Why this works
It uses the appropriate forecast uncertainty concept and checks calibration.
Follow-up to practice
How would you evaluate whether the interval is useful?