Adstock

The standard form is geometric adstock: this week's effect equals this week's spend plus a fixed fraction of last week's effect. That fraction is the decay rate. A decay of 0.5 means half the effect survives each week, which gives a half-life of one week; a decay of 0.8 gives a half-life of about 3.1 weeks (log 0.5 / log 0.8 = 3.106). Brand-building channels like TV are modeled with higher decay than performance channels like paid search, whose effect is mostly spent by the click.

Robyn's documentation offers two shapes: geometric, one parameter, effect strongest immediately; and Weibull, two parameters, which can delay the peak so an ad's strongest effect lands weeks after exposure.¹ Meridian applies the same idea within its Bayesian model, estimating the decay from data with priors.² The choice matters: force a TV channel into a one-week memory and the model hands TV's delayed revenue to whichever channel spent steadily, corrupting both ROIs.

Adstock is often confused with carryover. Adstock is the mechanism (a decaying transformation of spend); carryover is the phenomenon (effects arriving after the spend period). Every adstock is a carryover model; not every carryover model is adstock.