Croston's Method, SBA and TSB
By MLAIA Data Science Ltd. · Published 13 July 2026
Croston's method is the classical forecasting technique for intermittent demand. Introduced by J. D. Croston in 1972, it separates an intermittent series into two components — the size of demand when it occurs, and the interval between demand occurrences — and applies simple exponential smoothing to each. Later research established that the original method is positively biased, leading to the Syntetos–Boylan Approximation (SBA) correction and, for items at risk of obsolescence, the Teunter–Syntetos–Babai (TSB) variant.
Background
Croston observed that applying simple exponential smoothing (SES) directly to an intermittent series produces a systematically distorted forecast: the estimate jumps immediately after each demand occurrence and then decays through the zero periods, so it is highest just after demand has been satisfied and lowest just before the next demand is likely. His 1972 paper, "Forecasting and stock control for intermittent demands" (Operational Research Quarterly), proposed decomposing the series instead.
How the method works
Let z denote the size of a non-zero demand and p the number of periods since the previous non-zero demand (the inter-demand interval). Croston's method maintains smoothed estimates of both, updated only in periods where demand occurs:
ẑt = α·zt + (1 − α)·ẑt−1 p̂t = α·pt + (1 − α)·p̂t−1
where α is a smoothing constant (typically 0.05–0.2 for slow-moving items). In periods with zero demand, both estimates are left unchanged. The forecast of mean demand per period is the ratio:
ft = ẑt / p̂t
Intuitively: "when demand comes, it averages ẑ units, and it comes every p̂ periods, so the average demand rate is ẑ/p̂ per period." Unlike SES on the raw series, this estimate is stable through runs of zeros and does not spike after each occurrence.
The positive bias and the SBA correction
Croston assumed that the expected value of the ratio ẑ/p̂ equals the ratio of the expected values. It does not: because the interval estimate p̂ appears in the denominator, and the expectation of 1/p̂ exceeds 1/E[p̂] (a consequence of Jensen's inequality), the method systematically over-forecasts the demand rate.
Syntetos and Boylan quantified this bias and proposed a simple correction, now known as the Syntetos–Boylan Approximation (SBA). The SBA forecast multiplies Croston's estimator by a deflation factor that depends on the smoothing constant used for the intervals:
ftSBA = (1 − α/2) · ẑt / p̂t
The correction is approximately unbiased, and in the empirical comparison reported in Syntetos and Boylan (2005, International Journal of Forecasting) it outperformed the original method across a large sample of intermittent series. SBA is widely regarded as the sensible default whenever Croston-style forecasting is used, and the ADI = 1.32 / CV² = 0.49 classification cutoffs were themselves derived from the regions where SBA's expected error beats Croston's.
The TSB variant and obsolescence
Croston's method and SBA share a structural weakness: their estimates update only when demand occurs. If an item stops selling entirely — the classic path to obsolescence — the forecast stays frozen at its last value forever, and any stock policy driven by it will keep recommending inventory for a dead item.
Teunter, Syntetos and Babai (2011, European Journal of Operational Research) addressed this with the TSB method. Instead of smoothing the inter-demand interval, TSB smooths the probability of demand occurrence, and it updates this probability in every period — downward through runs of zeros, upward when demand appears:
d̂t = β·dt + (1 − β)·d̂t−1 ft = d̂t · ẑt
where dt is 1 in a period with demand and 0 otherwise, and β is its smoothing constant (demand size ẑ is still updated only on occurrence). Because d̂ decays geometrically through zero-demand periods, the TSB forecast declines toward zero for items whose demand is drying up — making it the standard choice for portfolios with significant obsolescence risk.
When each variant applies
| Method | Best suited to | Caveat |
|---|---|---|
| Croston (1972) | Historical baseline; teaching the decomposition | Positively biased — SBA dominates it in practice |
| SBA (2005) | Stationary intermittent or lumpy items | Forecast never decays if demand stops |
| TSB (2011) | Items with declining demand or obsolescence risk | Slightly biased; needs a second smoothing constant |
Limitations
- A rate, not a distribution. All three methods output a mean demand per period. Setting safety stock and reorder points requires the distribution of demand over the lead time, which must be assumed (Poisson, negative binomial, gamma) or estimated empirically, e.g. by bootstrapping (Willemain, Smart & Schwarz, 2004).
- No trend or seasonality. The decomposition assumes a stationary pattern; systematic trend or seasonality must be handled separately if present.
- Timing is not forecast. The methods say how much demand to expect per period on average, not in which period the next demand will land.
- Parameter sensitivity. Results depend on the smoothing constants; very short histories give unstable size and interval estimates.
References
- Croston, J. D. (1972). Forecasting and stock control for intermittent demands. Operational Research Quarterly, 23(3), 289–303.
- Syntetos, A. A., & Boylan, J. E. (2005). The accuracy of intermittent demand estimates. International Journal of Forecasting, 21(2), 303–314.
- Teunter, R. H., Syntetos, A. A., & Babai, M. Z. (2011). Intermittent demand: linking forecasting to inventory obsolescence. European Journal of Operational Research, 214(3), 606–615.
- Willemain, T. R., Smart, C. N., & Schwarz, H. F. (2004). A new approach to forecasting intermittent demand for service parts inventories. International Journal of Forecasting, 20(3), 375–387.