The final lesson closes the track by separating exact mechanics from empirical claims. The table is true by construction, and the boundary is just as important as the arithmetic.
highlighted = computed this step
Exact table
The table aligns the raw row, MA(3), and ES with alpha 1/2. Motivation: putting the formulas on the same periods makes their arithmetic differences visible without pretending to score them.
same periods, different exact formulas
MA row
The moving-average row ends at 19/3. Why: that value is the last recomputed three-value window average, so it depends only on the final window.
MAlast=19/3
ES row
The exponential-smoothing row ends at 51/8. Interpretation: that value is the last displayed recurrence output, carrying the prior state forward through exact fraction arithmetic.
ESlast=51/8
Recomputed comparison
If the last observed value is changed to 9, the exact recompute gives naive output 9, MA ending value 20/3, and ES ending value 55/8. Why: changed inputs change formula outputs, but still do not prove predictive accuracy.
recompute: 9,20/3,55/8
Honesty boundary
Honesty note: Forecast accuracy is empirical and deferred; it needs held-out data, error metrics, and process assumptions. The exact core here is the arithmetic mechanics. Pixel positions are rounded for layout; every number shown is exact.