History becomes signal.
One week at a time.

The laboratory builds a deterministic series with a seeded linear congruential generator. Weekly demand is the starting demand times a linear trend, an additive seasonal wave and zero-mean uniform noise. The series is synthetic throughout, so the data requirement is visible without pretending to hold a factory’s sales ledger. The same seed reproduces the same demand.

The forecast origin is fixed after week 104. Every fit predicts the same unseen weeks to its right. This is a controlled history-length experiment, not a real-time backtest with a changing calendar.

The history slider decides how many immediately preceding weeks the models receive, revealing older observations towards the left. The error curve is calculated at every whole week of training history. No smoothing makes it fall, so it can rise.

The naive method repeats the last observation. The moving average repeats the mean of the last four; it does not feed its forecasts back into the mean. Both are deliberately simple comparators, and older history cannot change their inputs once four observations exist.

Additive Holt-Winters separates level, trend and seasonal offsets. The first-cycle mean initialises the level. The change between the first two cycle means, divided by cycle length, initialises the trend. The first cycle’s deviations initialise the seasonal offsets, and the second cycle onwards updates them. The forecast extends level plus trend and repeats the latest seasonal offsets, with negative values clipped to zero.

A coarse grid tries alpha 0.15, 0.35, 0.65 and 0.90, beta zero, 0.10 and 0.30, and gamma-star 0.05, 0.25 and 0.60, and keeps the smallest one-step squared-error sum after the first two cycles. The unseen window never selects parameters. The method needs two complete cycles, 26 weeks: a laboratory rule, not a universal guarantee of adequate data.

The fans do not promise coverage at a stated probability. Residuals can understate uncertainty when the model is wrong, and the square-root widening rule is a teaching convention. A clean synthetic seasonal signal can make a seasonal method look unusually good. Structural breaks, holidays, product substitution, promotion timing and stockout-censored orders are absent. One seed and one origin cannot establish an expected commercial benefit.

The cost proxy penalises forecast mismatch with one unit cost for excess and shortage. It does not simulate an inventory policy, safety stock, lost-sales recovery or purchasing, and it estimates no revenue, cash release, payback or investment return. Replace the symmetry with measured carrying, markdown and shortage costs in a real inventory study.

MAPE can be unstable near zero and cannot be used where actual demand is zero; the synthetic floor prevents that division here. A manager can use the page to frame a data-collection pilot, an engineer can inspect the equations, and an investor can see which operating evidence is still missing.