Predict, test, and explain
Experiments with consequences
Record what you expect before changing an assumption. Use the result to revise the argument.
A decision before its outcome
Choose a reference procedure, record its forecast, then advance the information clock. The ledger retains the decision you actually made.
Texas residential electricity sales
Fixed vintage · illustrative two-month release lag · million MWh
Loading fixed teaching data
Reference forecasts use admitted history. The 60-month calendar option is fixed throughout this room; the project separately selects its repair on a later boundary. This is ungraded exploration.
The ledger stays in this page's memory until you export it or leave. It is not uploaded.
Persistence and forecast risk
Set persistence to −0.5. The response changes sign each period; the error variance keeps accumulating squared weights.
Values used in both graphs
| Horizon | Response, outcome units | Variance, squared units |
|---|---|---|
| 0 | 1.000000 | 0.000000 |
| 1 | 0.700000 | 1.000000 |
| 2 | 0.490000 | 1.490000 |
| 3 | 0.343000 | 1.730100 |
| 4 (selected) | 0.240100 | 1.847749 |
| 5 | 0.168070 | 1.905397 |
| 6 | 0.117649 | 1.933645 |
| 7 | 0.082354 | 1.947486 |
| 8 | 0.057648 | 1.954268 |
| 9 | 0.040354 | 1.957591 |
| 10 | 0.028248 | 1.959220 |
| 11 | 0.019773 | 1.960018 |
| 12 | 0.013841 | 1.960409 |
Original analytic teaching example. Parameters are known and innovation variance is one. These are conditional variances under conditional homoskedasticity; constant unconditional second moments support the same values as unconditional mean-squared errors.
Compare quarterly averaging with sampling every third month →
JavaScript enables the controls. The printed lecture includes the analytic curves and hand calculations.
Can the future alter a past estimate?
Keep observations through date 20 fixed and change the next two records.
The centered five-period mean admits dates 21 and 22. The trailing three-period mean admits only dates 18–20.
One covariance, several shock stories
Rotate a covariance factor while holding the observed covariance fixed.
Changing an impact pattern without changing covariance exposes an identification ambiguity. An economic shock needs additional assumptions.
A surprise changes the next risk forecast
Hold the mean at zero and update a GARCH variance after a realized return surprise.
The normal quantile is conditional on a distributional assumption. The same variance with heavy-tailed shocks can imply a different risk threshold.