Extrapolating a fading lift to its steady state

Question

A feature's measured lift is decaying as novelty wears off. The weekly treatment lifts are: week 1 = 9%, week 2 = 5%, week 3 = 3%, week 4 = 2%. The team wants the durable, long-run lift (the steady state the novelty is settling toward), not the inflated early numbers.

Estimate the long-run steady-state lift.

Accepted Answer

Model the decay as approaching a floor. Novelty effects fade in a roughly geometric way: each week the "extra" lift above the true long-run level shrinks by about the same fraction. So write the weekly lift as 	ext{lift}t = L + A \cdot r^{\,t}, where L is the durable steady-state lift, and A \cdot r^{t} is the fading novelty bonus that shrinks toward zero. We just need to find L. Find the common ratio using the gaps between weeks. Look at how much the lift drops each week: - Week 1 to 2: 9 	o 5, a drop of 4. - Week 2 to 3: 5 	o 3, a drop of 2. - Week 3 to 4: 3 	o 2, a drop of 1. Each drop…

Extrapolating a fading lift to its steady state

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