I am trying to optimize marketing spend across multiple websites i.e., Nanigans (Facebook), Google, etc, to increase customer conversion (purchasing). Each ad placement results in two things: new users signing up and purchasing and existing users seeing an ad and purchasing again.
For example, for Nanigans I might spend X for new user acquisition, Y for re-targeting, and Z for App installs. These are my input variables (Spend). My output variables are revenue that resulted from X, Y, and Z. I have daily time series data for all of the inputs and outputs across all websites. There is a catch. Advertisements meant for New User acquisition might be seen by existing customers.
What is the best statistical technique to solve this problem? How would I solve this problem in R?