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I am running a Market Mix model. There is a general practice in the industry to create an ad stock variable for media variables (like TV). I came across polynomial distributed lag model. I was thinking to used polynomial distributed lag instead of creating Adstock variables. Can anyone tell me whether should I move ahead with polynomial distributed lag or to continue with adstock variables?

anujk
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    Could you explain what is meant by Adstock variable in statistical terms? Wikipedia reads like it is some kind of distributed lag model, like the Kyock transformation? – IMA Jun 11 '13 at 14:05
  • Here is an example of adstock variable...http://mpra.ub.uni-muenchen.de/7683/4/Adstock_Model.pdf – anujk Jun 11 '13 at 14:53
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    This post may turn out somewhat unfair maybe but reading this paper you posted it seems that Adstock models are just renamed statistical models. The Simple Decay-Effect Model, invented by someone named Broadbent, is just a regular ADL(1) model, which is a combination of Autoregressive model with another exogenous variable, possibly lagged. Depending on the transformation of the T variable, you get the other models in that paper which are to be estimated by Least Squares, there is no consideration given if this is proper. I dunno man. I would definitly switch to proper regular models asap. – IMA Jun 11 '13 at 15:15

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The adstock variable is used by lots of consulting companies in the Marketing Mix space. If you are still interested in using adstock variables then you have to know/guess what adstock rate to use. I use Least Squares to analytically derive that rate base on the data: http://analyticsartist.wordpress.com/2014/01/31/adstock-rate-deriving-with-analytical-methods/

user38472
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    your suggested method doesn't seem to account for autocorrelation - i.e. values for the response will be more similar the closer together in time the observations are, violating any assumptions of independent data points. Would it be better to e.g. run multiple ARMA models, each with a different adstock rate, then use something like AIC to pick the final model? – jay Jul 11 '17 at 22:41
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Impulse response functions via VAR models are a great way to determine AdStock in an empirical manner. Alternatively, a simple ARDL model may do the trick - with the coefficients on the lag terms essentially mapping out the functional form of the 'AdStock'

Tom
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