How can I model the long-term (compounding) nature of my exogenous variables?

10 March 2016 0 8K Report

I am searching for a model and I feel like it has to be out there and relatively simple.

The relationship which I theorize and wish to test is that WebUsage is affected immediately by Television advertising in addition to the Television advertising having a long-term affect on WebUsage totals.

In other words, I would like to model WebUsage as a function of itself (ARIMA), exogenous variables (Television advertising).... IN ADDITION to having the affects of the exogenous variables having a direct affect on the parameters of the "ARIMA" process in some way. The idea is similar to compounding interest in a way.... If I added $500 a month to an account that earns 8 percent interest, the overall effect of each of those $500 impacts would actually be more that $500 since the account value would be growing. It is my theory that if a Television commercial drives 500 visitors to a website, a fraction of those visitors will return again at some point so the usage will compound and grow. So in a way, I want to be able to model out: 1) What is the immediate impact of Television Advertising? 2) What is the affects to Web Usage in the long-run? What type of model will allow me to determine this relationship?

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