Track 12 · Time Series and Forecasting · Lesson 11 of 11
Forecast uncertainty and limits
Compute approximate prediction intervals for simple forecasting methods, check them on held-out data, explain what they leave out, and communicate forecast uncertainty and structural breaks honestly.
A distributor ordered water heaters for 2022 using a forecast of about 2,600 units for January. Actual orders were 1,805. Nothing in a single number warned that such a miss was possible — a forecast without a range, and without a word about what could change, invites over-confidence.
A point forecast is the centre of what might happen. A prediction interval gives a range that should contain the future observation with a stated probability, such as 80% or 95%. It is wider than a confidence interval for a mean, because it must cover the noise of a single future value, and it widens as the horizon grows.
Included with a Formula Quest membership
It has 8 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Compute approximate prediction intervals for naive, seasonal naive and SES forecasts
- Explain why intervals widen with the horizon
- Check interval coverage on held-out data
- List what the formulas ignore and why real coverage is usually lower
- Communicate a forecast with its range, its miss rate and its limits, including structural breaks