Advertising Adstock Transformation with Maximum Period Decay.SAS

/* Macro Name  : Advertising Adstock with Maximum Period Decay
 * Written By  : Gabriel Mohanna
 * Date Created: Feb 21, 2014
 * Narrative   : Create Adstock transformation with Maximum Period Decay and compare to simple adstock transformation.
 *
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 * <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< Code is Poetry >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 * ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
 *
 * ***********************************************************************************************************************/

** Define Adstock Rate;
%let adstock = 0.50;

** Create Data;
data advertising;
    format Week 8. advertising 8.3;

    Week = _N_;
    input advertising @@;

datalines;
117.913 120.112 125.828 115.354 177.090 141.647 137.892   0.000   0.000   0.000   0.000 
  0.000   0.000   0.000   0.000   0.000   0.000 158.511 109.385  91.084  79.253 102.706 
 78.494 135.114 114.549  87.337 107.829 125.020  82.956  60.813  83.149   0.000   0.000 
  0.000   0.000   0.000   0.000 129.515 105.486 111.494 107.099   0.000   0.000   0.000 
  0.000   0.000   0.000   0.000   0.000   0.000   0.000   0.000
;
run;

** Calculate Advertising Adstock with 50% rate and 2 weeks period decay;
data Advertising;
	set Advertising;

	format advertising_adstock advertising_adstock_w_max_Decay 8.2;

	if _N_ = 1 then do;
        advertising_adstock = advertising;
        retain advertising_adstock;
    end;
    else do;
        advertising_adstock = sum(advertising, advertising_adstock * 0.5);
    end;

	advertising_adstock_w_max_Decay =  sum(0.5**0 * advertising, 0.5**1 * lag1(advertising), 0.5**2 * lag2(advertising), 0);
run;


** Graph Data;
ods graphics on;
ods html;
proc sgplot data=Advertising;
    vbar  week / response=advertising;
    vline week / response=advertising_adstock;
    vline week / response=advertising_adstock_w_max_Decay;
run;