Forecasting and Prediction Intervals

Artificial Intelligence and Data Science · CHAPTER 5 / 5

Level: introductory undergraduate · Study session: 15–20 minutes including practice.

Learning outcome: Separate point forecasts from uncertainty and evaluate by time.

Before you begin: Complete earlier chapters in this discipline; revise algebra and units as needed.

1. Understand the idea

A point forecast estimates a single future value. A prediction interval aims to cover a stated fraction of future observations under the evaluation conditions. Check empirical coverage and interval width over held-out time windows. Quantile forecasts should preserve order and use inputs available before the forecast origin.

2. Write the model

Coverage = observations inside interval / evaluated observations

Define the symbols from the worked case before substituting values. Keep units consistent, record the assumptions and round only after the calculation.

3. Follow a worked example

For intervals [8,12], [9,13], [10,14] and observations 10,14,12, two of three observations are covered: 66.7%. Three cases cannot establish reliable calibration.

4. Explore the model

Figure: calculated teaching cases; straight segments connect sampled points, not experimental observations. Read exact values below.

Illustrative scenario sweep — synthetic educational data
Case	Interval	Observed
1	8–12	10
2	9–13	14
3	10–14	12

Count coverage, widen each interval by one unit, and recalculate. Wider intervals can cover more while becoming less informative.

5. Reproduce it yourself

Copy the input cases into Excel or a notebook and name each quantity and unit.
Recalculate each result from the stated equation or rule. For qualitative cases, explain the state or partition decision instead.
Change one input, predict the direction of change, then calculate again.
Write one sentence explaining where the model stops being valid.

6. Check your understanding

Is a 90% interval guaranteed to contain every future value?

Reveal the answer and check your work

No. Its target is coverage across repeated comparable predictions.

Compare your result, units and reasoning. If they differ, return to the equation and test the worked case first.

7. Common mistake

Do not report interval reliability from a tiny illustrative sample.

Further study and academic note

Explore the discipline reference and further learning resources. This is an original IIMEEE introductory teaching note with synthetic examples; it is not a peer-reviewed research result or a professional design specification. Figures were constructed from the listed teaching cases. Resource links support further study and do not imply endorsement.