http://drunks-and-lampposts.com/2012/01/08/recovering-the-parameters-in-a-marketing-mix-model/

Generating Artificial Sales Data.r

# *--------------------------------------------------------------------
# | FUNCTION: create_test_sets
# | Creates simple artifical marketing mix data for testing code and
# | techniques
# *--------------------------------------------------------------------
# | Version |Date      |Programmer  |Details of Change
# |     01  |29/11/2011|Simon Raper |first version.
# *--------------------------------------------------------------------
# | INPUTS:  base_p         Number of base sales
# |          trend_p        Increase in sales for every unit increase
# |                         in time
# |          season_p       The seasonality effect will be
# |                         season_p*temp where -10<temp<10
# |          ad_p           The coefficient for the adstock
# |          dim            The dim parameter in adstock (see below)
# |          dec            The dec parameter in adstock (see below)
# |          adstock_form   If 1 then the form is:
# |                         ad_p*(1-exp(-GRPs/dim)+dec*adstock_t-1)
# |                         If 2 then the form is:
# |                         ad_p*(1-exp(-(GRPs+dec*GRPs_t-1)/dim)
# |                         Default is 1.
# |          error_std      Standard deviation of the noise
# *--------------------------------------------------------------------
# | OUTPUTS: dataframe      Consists of sales, temp, tv_grps, week,
# |                         adstock
# |
# *--------------------------------------------------------------------
# | USAGE:   create_test_sets(base_p,
# |                           trend_p,
# |                           season_p,
# |                           ad_p,
# |                           dim,
# |                           dec,
# |                           adstock_form,
# |                           error_std)
# |
# *--------------------------------------------------------------------
# | DEPENDS: None
# |
# *--------------------------------------------------------------------
# | NOTES:   Usually the test will consists of trying to predict sales
# |          using temp, tv_grps, week and recover the parameters.
# |
# *--------------------------------------------------------------------

#Adstock functions

 adstock_calc_1<-function(media_var,dec,dim){
  length<-length(media_var)
	adstock<-rep(0,length)
	for(i in 2:length){
		adstock[i]<-(1-exp(-media_var[i]/dim)+dec*adstock[i-1])
	}
 adstock
 }

adstock_calc_2<-function(media_var,dec,dim){
	length<-length(media_var)
	adstock<-rep(0,length)
	for(i in 2:length){
		adstock[i]<-1-exp(-(media_var[i]+dec*media_var[i-1])/dim)
	}
adstock
}

#Function for creating test sets

create_test_sets<-function(base_p, trend_p, season_p, ad_p, dim, dec, adstock_form, error_std){

  #National level model

  #Five years of weekly data
  week<-1:(5*52)

  #Base sales of base_p units
  base<-rep(base_p,5*52)

  #Trend of trend_p extra units per week
  trend<-trend_p*week

  #Winter is season_p*10 units below, summer is season_p*10 units above
  temp<-10*sin(week*3.14/26)
  seasonality<-season_p*temp

  #7 TV campaigns. Carry over is dec, theta is dim, beta is ad_p,
  tv_grps<-rep(0,5*52)
  tv_grps[20:25]<-c(390,250,100,80,120,60)
  tv_grps[60:65]<-c(250,220,100,100,120,120)
  tv_grps[100:103]<-c(100,80,60,100)
  tv_grps[150:155]<-c(500,200,200,100,120,120)
  tv_grps[200:205]<-c(250,120,200,100,120,120)
  tv_grps[220:223]<-c(100,100,80,60)
  tv_grps[240:245]<-c(350,290,100,100,120,120)

  if (adstock_form==2){adstock<-adstock_calc_2(tv_grps, dec, dim)}
  else {adstock<-adstock_calc_1(tv_grps, dec, dim)}
  TV<-ad_p*adstock

  #Error has a std of error_var
  error<-rnorm(5*52, mean=0, sd=error_std)

  #Full series
  sales<-base+trend+seasonality+TV+error

  #Plot
  #plot(sales, type='l', ylim=c(0,1200))

  output<-data.frame(sales, temp, tv_grps, week, adstock)

  output

}