Choosing a Forecast After a Market Shift
A consumer-goods planner has six months of history and two candidate forecasts. Actual monthly demand was 420, 455, 480, 470, 510, and 495 units. Forecast A, a three-month moving average, produced 430, 435, 445, 460, 470, and 490. Forecast B, Holt exponential smoothing with trend, produced 425, 450, 470, 490, 520, and 520. In month 5 a national retailer opened two stores in the region and a competitor cut prices 15%. The planning team believes months 5 and 6 represent a new, flatter plateau rather than a spike, and that growth has stopped. Forecast bias is reviewed monthly; the tracking-signal trigger is plus or minus 4. The product carries a 30% annual carrying cost and stockouts cost roughly three times the margin per unit.
1. Compute MAD, running sum of forecast error, and the tracking signal for both forecasts.
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Error defined as Forecast minus Actual.
Forecast A
| Period | Actual | Fcst | Error | Abs |
|---|---|---|---|---|
| 1 | 420 | 430 | +10 | 10 |
| 2 | 455 | 435 | -20 | 20 |
| 3 | 480 | 445 | -35 | 35 |
| 4 | 470 | 460 | -10 | 10 |
| 5 | 510 | 470 | -40 | 40 |
| 6 | 495 | 490 | -5 | 5 |
| Sum | -100 | 120 |
MAD = 120 / 6 = 20.0. RSFE = -100. Tracking signal = -100 / 20 = -5.0, outside the -4 trigger.
Forecast B
| Period | Actual | Fcst | Error | Abs |
|---|---|---|---|---|
| 1 | 420 | 425 | +5 | 5 |
| 2 | 455 | 450 | +5 | 5 |
| 3 | 480 | 470 | -10 | 10 |
| 4 | 470 | 490 | +20 | 20 |
| 5 | 510 | 520 | +10 | 10 |
| 6 | 495 | 520 | +25 | 25 |
| Sum | +45 | 75 |
MAD = 75 / 6 = 12.5. RSFE = +45. Tracking signal = 45 / 12.5 = +3.6, inside the trigger but climbing in the wrong direction: the last three periods alone give RSFE of +55 on a recent MAD of 18.3, a recent tracking signal of about +3.0.
Forecast B halves the absolute error and stays inside the control limit; Forecast A is biased low by an average of 16.7 units per month and has already breached the trigger.
2. Which forecast would you deploy, what structural changes would you make, and how would you monitor it?
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Deploy B, but not unchanged. Choosing on MAD alone gives the right answer for the wrong reason. The decision has to be judged on the error pattern, because the two forecasts fail in different directions and those failures carry different costs here.
- A is systematically low (RSFE -100 over six months). A low bias with a stockout penalty roughly three times the margin per unit is the more expensive failure mode, and a moving average cannot do anything about it: it lags a level shift by its own window.
- B is technically in control but its error has flipped sign in the last three periods (+20, +10, +25). That is the signature of a linear trend extrapolating through a plateau. If the team is right that growth has stopped, B will keep over-forecasting, and the penalty shifts from stockouts to inventory carrying cost.
Structural changes
- Damp or freeze the trend component. Reduce the trend smoothing constant sharply, or cap the trend increment, once a structural break is suspected. A damped trend is the standard remedy for exactly this failure.
- Re-estimate the level from the post-shift periods (months 5 and 6) rather than carrying a level built on the pre-shift slope.
- Shorten the evaluation window to three rolling periods while the new plateau is forming; six-period MAD hides a two-period break.
- Add causal inputs that move ahead of the series: competitor price index and store count in the region, so the shift is anticipated rather than absorbed.
Monitoring. Keep the tracking signal at plus or minus 4, but review it monthly against the rolling three-period window, and add a second check for sign reversal: two consecutive periods of same-direction error after a structural change should trigger a model reset regardless of the aggregate figure. Recompute the stockout-versus-carrying cost weighting at the next review, because a plateau changes the asymmetry that justified B in the first place.