Intermittent · Free
Croston
Split size and interval; update only when demand occurs.
What it assumes
Demand size and interval are separate SES processes; updates only on nonzero demand.
When to use
Spare parts / intermittent SKUs with many zeros.
When to avoid
Smooth daily sales, or dying SKUs (interval never updates on zeros — use TSB).
Knobs
ŷ = z / p with α on size and interval.
How it works
When most periods are zero, averaging the zeros drags SES toward nothing. Croston smooths two series: demand size on nonzero periods, and the interval between those periods. The point forecast is size / interval. Updates happen only on a hit, so a dying SKU whose zeros never stop can keep an outdated interval — TSB is the obsolescence tool. Smooth daily sales should stay on SES.
Sample forecast question
A spare part sold in only four of twelve weeks. What is Croston’s mean weekly demand forecast for the next four weeks?
Step-by-step on these numbers
| Period | Actual | Fitted |
|---|---|---|
| W1 | 0 | 0 |
| W2 | 0 | 0 |
| W3 | 6 | 6 |
| W4 | 0 | 2 |
| W5 | 0 | 2 |
| W6 | 4 | 2 |
| W7 | 0 | 1.97 |
| W8 | 0 | 1.97 |
| W9 | 0 | 1.97 |
| W10 | 8 | 1.97 |
| W11 | 0 | 1.97 |
| W12 | 5 | 1.97 |
| Period | Forecast | 95% interval |
|---|---|---|
| W13 | 1.99 | -3.06 – 7.04 |
| W14 | 1.99 | -5.15 – 9.13 |
| W15 | 1.99 | -6.76 – 10.73 |
| W16 | 1.99 | -8.11 – 12.09 |
Parameters the engine found
alpha= 0.050level= 1.987z= 5.955p= 3
The question
A spare part sold in only four of twelve weeks. What is Croston’s mean weekly demand forecast for the next four weeks? Sample weeks: W1=0, W2=0, W3=6, W4=0, W5=0, W6=4, W7=0, W8=0, W9=0, W10=8, W11=0, W12=5 (units).
Split size and interval
Nonzero demands: W3=6, W6=4, W10=8, W12=5. Zeros are not averaged in as “small demand” — they only stretch the interval.
Updates on hits only
SES with α = 0.050 (grid on {0.05…0.40}) updates size z and interval p when y_t > 0. After the sample: z = 5.955, p = 2.997.
Mean rate
Point forecast = z/p = 5.955/2.997 = 1.99 per week, held for every horizon.
Forecast
W13: 1.99; W14: 1.99; W15: 1.99; W16: 1.99.
Interval
Residual σ = 2.576. For h = 1 the 95% band is [-3.06, 7.04] around 1.99. The engine labels this a residual-Gaussian heuristic (σ√h), not a simulation interval.
Graph of this sample
The chart plots the canned table on this page (actuals, in-sample fitted, forecast, 95% interval). Not your Excel series. Free analysis never uploads raw data.
Educational only. Not investment, weather, or operational advice. In the add-in, rank is rolling-origin MASE — “best supported among candidates on this series.”