Adstock transforms an exposure series into a stock of potential effect.
Adstock transforms an exposure series into a stock of potential effect. A geometric model imposes an immediate maximum and constant decline; Weibull can represent a delayed peak and more flexible decay. Selection must not only improve fit: half-life and shape must fit channel, creative, data frequency and available experiments.
Decision and method.
Retain media memory only when its profile improves out-of-sample validation without creating durable effect incompatible with operations. Compare immediate weight, peak week, half-life and mass after four or eight weeks for each kernel family. Set parameter bounds from campaign duration, purchase frequency, tests and media knowledge before optimisation. Test whether the kernel predicts variation periods and retains plausible contribution; re-estimate with trends, seasonality and alternative events. A collapsing half-life signals that adstock had captured an omitted factor.
Worked example.
Geometric adstock is Aₜ = Xₜ + 0.6 × Aₜ₋₁. An impulse of 100 produces 100, 60, 36, 21.6 then 13. Half-life = ln(0.5) ÷ ln(0.6) = 1.36 weeks. Theoretical total mass is 100 ÷ (1 − 0.6) = 250 transformed exposure units. This is acceptable for a short effect. An estimate of 0.9, or 6.58 weeks half-life, needs strong evidence and trend tests.
Checks and limits.
Publish half-life, peak week and area per channel; justify ranges before fitting; require out-of-sample improvement and stability against trend and season controls. Aggregated data struggle to identify adstock, saturation and seasonality together; a weekly kernel may mix creatives and delivery strategies; a short experiment weakly informs a long tail.
Resources and sources.
Download adstock kernels. Related: model diminishing returns, validate MMM mechanisms, constrain with experiments. Sources: Koyck (1954); Broadbent (1979); Jin et al. (2017).