Is adstock a myth I have been seeing a lot of multiple regression models that have an adstock term. This term is a decay function of media. The idea is that when media is turned off, there is a decay in its effect that may last up to 2 weeks! 
I am skeptical of adstock. I think that when marketing mix models are solely multiple regression models they ignore autocorrelation and the effect that they perceive as adstock is mostly autocorrelation. 
Further, from Rob Hyndman's Forecasting Book he states that 

Behavioural theory tells us that intentions predict behaviour if the intentions are measured just before the behaviour.

Therefore the idea that purchase-intent is still lingering 2 weeks after seeing a 15 sec commercial is suspect.
Are there any papers addressing adstock in the presence of autocorrelation? 
Further Adstock Reading:


*

*Related Thread

*Example Of Calculating Adstock In R

*Advertising Adstock Paper

*Marketing Mix Models In R
 A: I don't understand your argument. Would you say that the moment the ad is off its effect is completely erased instantaneously? 
That probably is not a reasonable assumption. So, some kind of an temporal decay of ad's effect sounds very reasonable to me. 
In physics of radioactivity there's a very similar half-life concept: it's time when the half of nuclei are gone. For instance, uranium 238 has 4.5 mln years when half of them are gone. The same for Cesium 137 is 30 years and Polonium 214 is less than a millisecond.
My point is that having adstock or similar decay variable doesn't contradict your intuition. Suppose you think the ad's effect is gone in a day, then set its half life to one day or one hour, whatever fits your data. It doesn't have to be two weeks for every ad, each ad may/should have its own half life.
I agree with your observation that marketing mix models tend to be cross sectional regression models. I'm not sure why. You can't do time series on them, so more advanced analysis must have to be longitudinal models, such as mixed effects. I believe that ideally they should account for autocorrelation, but it's very difficult. 
A: This is just for posterity. I found this where advertising was used to change road safety behavior. In it they considered adstock, but since their estimated equations already implied half life effect they did not see much benefit by including adstock measure.

our estimated equations
implicitly incorporate a
half life
type of effect
so
there
is nothing to be gained by adopting an Adstock measure

