The right demand forecasting model, SKU by SKU

The comparison

Scope of the test. Demand classification and automatic season detection use the supplied history before the backtest. Each model is fitted only on its training block, but the scores are conditional on that earlier candidate selection. They are not an independent evaluation of the complete selection process or a guarantee of future accuracy.

Every model starts from the same month of history, so the accuracy figures in the table were measured on the same data.

At each forecast origin a model sees only the history available at that moment and predicts forward. Move the origin along and you get a set of honest out-of-sample errors.

What usually goes wrong elsewhere is that different models need different amounts of history to start, so each gets scored from its own earliest origin — and accuracy measured on different data ends up in the same column. Here every eligible model starts at the same origin. If including seasonal models would leave too few evaluation folds, they are excluded outright and the page says so. The fold count sits next to every model so you can check.

Classification

ADI and CV² decide which models are allowed to compete for a SKU. They never decide the winner.

Average demand interval and the variability of the non-zero order sizes place each SKU in one of four quadrants — smooth, erratic, intermittent, lumpy — on the Syntetos–Boylan–Croston (2005) scheme. Check a single row with the ADI and CV² calculator. Smooth and erratic series go to the continuous-demand family; intermittent and lumpy go to the intermittent estimators, and a continuous-demand model cannot win there however good its error looks.

The eleven models

Seven for regular demand, four for intermittent. All published, all named.

Regular demand: Naive · Moving average (3) · SES / ETS(A,N,N) · Holt linear trend · Holt-Winters additive · ARIMA(1,1,0) with drift · seasonal naive with drift.

Intermittent demand: Croston · SBA · TSB · ADIDA.

Smoothing constants are fitted to each SKU rather than pinned at textbook defaults, and the fitting only ever sees the training block of the fold it is in. Ranking uses one-month-ahead rolling-origin error with a penalty for persistent bias; the score is in the table beside the error. The 3-, 6- and 12-month forecasts are not separate horizon-specific model selections.

The range

A P10–P90 that has been tested for coverage against held-out data, not asserted.

The spread of the rolling error is measured at each horizon from the folds that genuinely reach it, and grown beyond the last horizon the data supports — the chart marks that switch with hollow bars. Intermittent and lumpy series get a bootstrap instead of a normal curve, because their demand has a large lump at zero. The page says which method produced the numbers on screen.

Calibration. A stated 80% range is worth nothing unless it holds about 80% of the time. Across 120 synthetic histories in each of six demand families — flat, trending, seasonal, random-walk, lumpy and intermittent — fitted on 36 months and scored against the following 12, the published range contained the outcome between 74% and 89% of the time, monthly and by horizon. These synthetic results do not guarantee coverage on an individual real-world SKU.

What the sheet should look like

SKU in column A, one column per month after it, oldest first. Zeros are data; keep them.

One row per SKU. Column A is the SKU code. Every other demand column represents one month, oldest first. Date headers (2025-01, Jan 2025, or Excel dates) must be consecutive, with no duplicates or missing months. Undated headers must be M1, M2, M3… (or 1, 2, 3…), and require a last actual month in the workspace. Headerless sheets also require this date. One optional column, headed Season, sets that SKU's cycle length — for example 3 for a quarterly pattern. It is set aside before the months are read, so it can sit anywhere after column A. Leave it blank to use the season length chosen on the page.

Zeros are data. A zero means no demand that month and the classification depends on it, so leave them in rather than deleting the cell — deleting it shifts every later month back by one.

Blanks. Missing demand cells anywhere in a row are reported, including the first and last periods. They are never removed or converted to zero. Resolve missing observations in the source data. For a newly launched SKU, analyse its actual history separately with the correct last actual month; do not invent pre-launch zero demand.

Negatives stop that SKU from being analysed. Resolve returns and credits in the source data before importing; the tool never silently replaces them with zero.

How much history. Ten months minimum, twenty-four before the backtest is worth much. A seasonal model needs two full cycles plus four evaluation folds — about 28 months for an annual cycle — or it is excluded and the page says so.

Known limitations

Where the numbers get thin, stated up front.

The seasonal entry is a baseline, not an order-searched SARIMA. The calibration study uses synthetic histories with clean structure; a real SKU with a regime change part-way through will be harder than anything in it. Intervals inherit the length of your history — with only a handful of folds the range is indicative, and the fold count is shown so you can judge it. Promotions, price changes, cannibalisation and new-product effects are not modelled; the scenario tool is where you put what you know and the history does not.

Sources

The cut-offs, the estimators, the error measures and the backtest design all come from published work, not house opinion.

1. Croston, J. D. (1972). Forecasting and stock control for intermittent demands. Operational Research Quarterly, 23(3), 289–303. The original size-and-interval method. Journal record
2. Syntetos, A. A. & Boylan, J. E. (2001). On the bias of intermittent demand estimates. International Journal of Production Economics, 71(1–3), 457–466. Croston's bias and the SBA correction. Journal record
3. Syntetos, A. A., Boylan, J. E. & Croston, J. D. (2005). On the categorization of demand patterns. Journal of the Operational Research Society, 56(5), 495–503. The ADI / CV² quadrants and the 1.32 and 0.49 cut-offs. Journal record
4. Kostenko, A. V. & Hyndman, R. J. (2006). A note on the categorization of demand patterns. Journal of the Operational Research Society, 57(10), 1256–1257. A refined boundary between Croston and SBA. Paper (PDF)
5. Hyndman, R. J. & Koehler, A. B. (2006). Another look at measures of forecast accuracy. International Journal of Forecasting, 22(4), 679–688. MASE, the scaled error in the model table. Paper (PDF)
6. 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. TSB, which keeps updating through zero-demand runs. Journal record
7. Hyndman, R. J. & Athanasopoulos, G. (2021). Forecasting: Principles and Practice, 3rd ed., section 5.10. OTexts. Rolling-origin (time-series) cross-validation. Online text