Adstock: choosing a media memory compatible with the observed mechanism.
Directly verifiable evidence
Primary sources to check the key claims.
- Meridian, model configuration (opens in a new tab)
Adstock specification, lags and model parameters.
Key distinctions
Three conditions before calculating.
A non-causal stock
Adstock is a structural transformation, not proof of an effect. A long memory can absorb trend, seasonality or competitive activity when those factors are poorly controlled.
Time scale
A weekly parameter does not transpose directly to daily data. Half-life, peak and area must be expressed in the time unit of the dataset.
Channel mechanism
Brand search, television, promotion and CRM do not share the same dynamics. Imposing a common kernel simplifies the model but can distort the contributions.
Method
Estimating a memory without letting the model invent the past
- 01Plot the impulse
Compare immediate weight, week of the peak, half-life and mass after four or eight weeks for each kernel family.
- 02Bound the parameters
Define ranges informed by campaign duration, purchase frequency, tests and media knowledge; the bounds must be published before optimisation.
- 03Validate out of period
Test whether the kernel predicts the periods of variation and keeps plausible contributions — a better internal fit is not enough.
- 04Test the confounders
Re-estimate with alternative trends, seasonalities and events; a half-life that collapses indicates that adstock was capturing an omitted factor.
Three responses to the same media impulse
A one-off spend of 100 is propagated over eight weeks by three kernels. Area, peak and half-life make the assumptions comparable.
A retention of 0.6 implies a half-life of 1.36 weeks
A geometric adstock is defined by Aₜ = Xₜ + 0.6 × Aₜ₋₁. An impulse of 100 produces 100, 60, 36, 21.6 then 13 units.
Half-life = ln(0.5) ÷ ln(0.6) = 1.36 weeks. The total theoretical mass is 100 ÷ (1 − 0.6) = 250 units of transformed exposure.
The parameter is acceptable for a short effect. An estimate of 0.9, that is a half-life of 6.58 weeks, would require strong evidence and tests against the trend.
Acceptance conditions
What must be true to act.
- 01
Half-life, week of the peak and area are published for each channel.
- 02
Parameter ranges are justified before fitting.
- 03
The kernel improves out-of-sample validation and not only the fit.
- 04
Stability is tested against several trend and season controls.
Limits
What this analysis does not prove.
- Aggregate data identifies adstock, saturation and seasonality simultaneously only with difficulty.
- A weekly kernel often mixes several creatives and delivery strategies.
- A short experiment informs the long-run tail imperfectly.
References
Works cited.
- Koyck, L. M. (1954), Distributed Lags and Investment Analysis.
- Broadbent, S. (1979), One Way TV Advertisements Work.
- Jin, Y. et al. (2017), “Bayesian Methods for Media Mix Modeling with Carryover and Shape Effects”.