The sum everyone needs
Some of the most important numbers in planning are not one period of a forecast but the sum of several: demand across a six-week lead time, revenue across a customer's lifetime, cash flow across a project. The point forecast of a sum is easy — add up the periods. The band around it is where things go wrong.
Two answers look obvious, and each is a textbook default.
Sum the bounds. Add the per-period lower bounds and call it a lower bound on the total. It feels conservative. It is actually the mathematical claim that every period misses together, in the same direction, every time — perfect correlation between periods.
Assume independence. The statistics-course route: variances add, so the band on the sum grows with the square root of the horizon. This is the assumption inside the classic safety-stock formula, and inside most NPV models.
The truth has to live between them — and where it lives is measurable, so we measured it.
What the backtests said
We replayed held-out history across our backtest suite and asked, for each assumption: does an 80% band on the cumulative total actually contain the real total 80% of the time?
| assumption | correlation | measured coverage at nominal 0.80 |
|---|---|---|
| independent periods | 0.0 | 0.33 – 0.51 |
| what we ship | 0.5 | on target, across all three engines |
| sum the bounds | 1.0 | 0.82 – 0.87 |
Independence is not a conservative simplification. On real forecast errors it is the most dangerous assumption in the room.
That first row deserves a second look: a nominal 80% band that covers a third of real outcomes. The reason is simple once said out loud — forecast errors persist. If period one comes in low because demand stepped down, period two is coming in low for the same reason. Errors that share a cause do not cancel, and the square-root formula is built entirely on them cancelling.
Summing the bounds fails far more gently: it overshoots. If you must pick a manual heuristic, pick that one — but know that its band is wider than its label, and every safety stock sized against it carries dead inventory.
What we ship
The accumulate option returns the cumulative path with a band built on the measured middle ground: partial correlation between periods, calibrated by backtest rather than assumed. The response says so — and if you override the correlation with your own assumption, the label flips, because your assumption should never be mistaken for our measurement.
{
"total": 24810,
"lower": 21050,
"upper": 28570,
"assumptions": { "correlation": 0.5, "measured": true }
}
One more rule, and it is the one we are proudest of: when a band's real coverage cannot be established for a series, no interval is returned at all, with the reason stated. A missing band is honest. A fabricated one is a liability with decimals.