Suppose I have a website which has some baseline hourly traffic. I also run TV advertising intermittently which drives up my web traffic. I want to determine how much effect my TV advertising is having in terms of driving up web traffic.
If I fit an ARMAX model with hourly TV advertising spend or impressions as exogenous variables, is it valid to claim that the AR terms represent the "baseline traffic" while the regression terms represent the traffic that should be attributed to TV advertising?
Here is some example code of what I'm trying to do:
library(forecast) xmat <- as.matrix(cbind(data[,c("AdSpend","Impressions")])) xvar <- data$WebSessions fit <- Arima(x=xvar, xreg=xmat, order=c(12,0,0), include.constant=FALSE) reg_terms <- fit$coef["AdSpend"] * data$AdSpend + fit$coef["Impressions"] * data$Impressions AR_terms <- fitted(fit) - reg_terms
I can then create a stacked area chart using AR_terms (the baseline hourly web traffic) and reg_terms (the TV attributed hourly traffic).
Is this a valid approach?
Thanks for the help.