The time unit is part of the parameter
Geometric adstock carries a fraction of previous exposure into the next period. A decay value of 0.5 means half the remaining impulse persists for one model period. If the data is weekly, the half-life is one week; if it is daily, the half-life is one day.
- Identify the period
- Convert decay to half-life
- Check the tail window
- Interpret exposure units
The adstock guide explains the transformation. This article turns its parameter into an assumption that a marketer can challenge in elapsed time.
The response you infer depends on transformation choices and what the data can separate. The how marketing mix models work learning path connects this idea to the assumptions, practical checks and next steps.
To work through the connected decisions, read Robyn hyperparameters: investigate estimates at the bounds and Podcast MMM: align ad delivery, lag and promo-code evidence.
Calculate the geometric half-life
For decay between zero and one, solve decay raised to h = 0.5. The half-life is h = log(0.5) / log(decay), measured in model periods. A decay of 0.5 gives one period. A decay of 0.8 gives approximately 3.11 periods. A decay of 0.9 gives approximately 6.58 periods.
For a hypothetical weekly model with decay 0.8, a single impulse of 100 leaves 80 after one week, 64 after two and 51.2 after three. These are transformed exposure units, not new pounds spent. Normalised implementations can rescale the sequence, so confirm the package definition before comparing coefficients.
Compare daily and weekly assumptions carefully
If persistence follows the same simple geometric process, a daily decay d corresponds to d raised to 7 over a week. A daily decay of 0.9 therefore retains roughly 0.478 after seven days. Copying 0.9 directly into a weekly model would imply much longer persistence.
This conversion describes an impulse-decay assumption, not a guarantee that daily and weekly fitted models are equivalent. Aggregation changes the timing of inputs, noise and interactions with saturation. A weekly spend total does not reveal which days the exposure occurred.
Check truncation and identification
Many implementations limit the number of lag periods. If the chosen window ends while a substantial tail remains, the effective transformation differs from an infinite geometric series. Show the remaining tail at the cutoff and explain the initial state at the beginning of the dataset.
A fitted long half-life can also compensate for trend, omitted variables or correlated campaigns. Compare reasonable lag assumptions and ask whether the available variation supports the distinction. The saturation guide matters because carryover and saturation jointly determine the response.
For a decision review, report the period, decay family, normalisation, maximum lag and implied half-life together. A single number labelled adstock is too ambiguous to compare across tools or datasets. Use an experiment or sensitivity analysis to challenge the mechanism rather than treating the fitted value as a directly observed fact.
Sources and further practice
This article’s worked example is illustrative, not a measured client result. Use the linked methodology to check the assumptions before applying it.