Cold-Start Forecasting for a Product With No History

Every forecasting method in this cluster estimates something from a series. A product launching next Tuesday has no series. The methods that work here all do the same thing — borrow from series that are not this one — and they differ in how much of your own data they let in and how quickly.

Why there is nothing to fit

Be precise about what is missing, because it is not just data volume. A seasonal model needs at least two full cycles to identify the seasonal component at all. An autoregressive model needs enough observations to estimate its coefficients with a standard error smaller than the coefficients. A pretrained model, as covered in zero-shot forecasting, removes the fitting step but still conditions on a context window, and a context of four observations conveys almost nothing, so it will return something close to a flat continuation.

So the cold-start problem is not solved by a cleverer algorithm applied to the same four numbers. It is solved by widening what counts as relevant data, which means deciding what makes two products comparable and being willing to defend that decision, since it is now the model.

Zero history: pool across the group

With no observations at all, the only forecast available is the behaviour of a group the new item belongs to. Define the group by attributes known before launch — category, price band, pack size, channel, region, whether it is a line extension of an existing product — and forecast the new item as the group’s typical launch, scaled by whatever the attributes say.

The workable version of this is a regression on attributes rather than a lookup of a group mean. Fit first-period demand across every past launch as a function of the attributes you will know for the new one, and use the fitted value. This handles a product that belongs to no existing group cleanly, because it interpolates between attributes instead of failing to match a bucket. It also gives you a residual spread across past launches, which is the only honest source of an interval at this stage: if past launches in this category came in anywhere between half and triple their predicted first month, that range is your forecast interval, and it is wide because the situation is genuinely uncertain rather than because the method is crude.

Two details do most of the work. Model the shape separately from the level: launch curves have a characteristic profile — a pipeline fill, a peak, a decay to a steady rate — and the profile is much more stable across products than the level is. And exclude the failures from the reference set only if you intend to forecast successes, which you usually do not, since the group of past launches includes the ones that did not work and so should your expectation.

A few days: scale an analogue curve

Once a handful of observations exist, they cannot estimate a shape but they can estimate a scale factor. Choose one or several analogue products, take their average normalised launch curve, and fit the single multiplier that best matches your observations so far.

analogue normalised curve, week 1..8 (fraction of week-8 rate)
  0.35  0.62  0.85  0.98  1.04  1.02  1.00  1.00

observed for the new product: week 1 = 21, week 2 = 40

scale from week 1:  21 / 0.35 = 60.0
scale from week 2:  40 / 0.62 = 64.5
least-squares scale over both:
  (21x0.35 + 40x0.62) / (0.35^2 + 0.62^2) = (7.35 + 24.8) / (0.1225 + 0.3844)
                                          = 32.15 / 0.5069 = 63.4

forecast week 5 = 63.4 x 1.04 = 65.9

One parameter estimated from two observations is a defensible thing to do; eight parameters from two observations is not, which is exactly why the shape is borrowed and only the scale is fitted. The scale estimate moves quickly at first and then settles, and watching it settle is a useful diagnostic in itself: a scale factor that is still moving by twenty per cent a week after six weeks means the analogue is wrong, not that the estimate needs more time.

A few weeks: shrink towards the group

The transition from borrowed to own data should be gradual rather than a switch on a date. The standard device is shrinkage: a weighted average of the item’s own estimate and the group estimate, with the weight determined by how much own data exists.

estimate = (n / (n + k)) x own_mean  +  (k / (n + k)) x group_mean

group mean (weekly units)          40
own mean over n = 3 weeks          62
k (shrinkage constant)              4

  (3/7) x 62 + (4/7) x 40 = 26.57 + 22.86 = 49.43

after 8 weeks of own data at the same level:
  (8/12) x 62 + (4/12) x 40 = 41.33 + 13.33 = 54.67

At three weeks the estimate sits nearer the group than the item; at eight it has moved most of the way to the item; the group never quite disappears. The constant k is the number of observations at which own and group data carry equal weight, and it is not arbitrary: in the empirical Bayes reading it is the ratio of within-item variance to between-item variance, so a category whose members differ wildly from each other gets a small k and rapid emancipation, and a category whose members behave alike gets a large k and stays pooled for longer. You can estimate both variances from your history of past launches, which turns the one free parameter into something derived.

The same structure appears whenever a hierarchy exists, and it is the reason a new store, a new region and a new SKU are the same problem with different groups. Where the new item also has to fit into an existing set of totals, the reconciliation step in hierarchical forecast reconciliation is what keeps it consistent with them.

What to watch while it warms up

• Distinguish no demand from no availability. A zero in week one because the product had not reached shelves is not evidence about demand, and feeding it in as a zero biases every estimate downward. Track distribution separately and forecast the rate per available outlet.
• Expect the pipeline fill to mislead. Initial shipments to stock shelves look like demand and are not repeated. If your history is shipments rather than sales, the first weeks are systematically high and the analogue curve must have been built from the same kind of data for the scaling to mean anything.
• Cannibalisation is a level effect on the neighbours. A launch that draws from an existing product changes that product’s series at a known date, which is a change point you can supply rather than discover.
• Intermittency arrives before seasonality. A slow new item generates mostly zeros, and a mean is the wrong summary of it. That is a different family of methods; see intermittent demand forecasting.
• Set the review date when you set the forecast. The useful question at week four is not whether the forecast was right but whether the analogue and the group still look like the right reference, and that question does not get asked unless somebody scheduled it.