I am trying to find the correlation between two time series, call them A and B. Let's pretend A has the number of successful advertising campaigns for each month for a company, and B has the company's revenue growth rates (year over year) each quarter. My hypothesis is that the effects of a successful advertising campaign would show up next quarter, and that there would be a lingering effect for about a year.
Based on my assumptions, would it be legitimate for me to try to cross-correlate the values in B and a moving average over a year shifted forward one quarter for the values in A? If not, why not, and what would be a legitimate way for me to test my hypothesis? I am using R, but am looking to make sure I am thinking about this correctly statistically.
Thanks so much for your help.