Adstock.

Adstock is the MMM component that mathematically models how an ad's effect persists past the week it runs, decaying gradually. The practical implication: a TV ad you saw this week may still be lifting sales four weeks later.

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An MMM that uses plain regression with 'weekly spend → weekly sales' can't see the delayed effect. Adstock models that delay:

Adstock_t = X_t + λ × Adstock_{{t-1}}

The decay rate λ varies by channel:

• Performance Search: λ ≈ 0.1 — effect dies fast (post-click memory is short).
• Display / Social: λ ≈ 0.3-0.4 — medium-term.
• TV: λ ≈ 0.5-0.7 — effect lingers for weeks.
• OOH (outdoor): λ ≈ 0.6-0.8 — longest-lived.

Ignore adstock and delayed-effect channels (TV, OOH) appear weaker than they are; the model assigns them low coefficients and their true contribution is lost.