Let's say I have a time series that shows daily traffic to my website. My website is getting more popular so there's a trend up, and the traffic is based on day of week so it's cyclical with a period of 7 days.
At a known date, I rolled out a new feature that was supposed to increase traffic to the site. What sort of test do I use to find out if there has been an effect after that point, and what the size of the effect was?
If there were no trend and I was dealing with non time-series data, I could just do a paired t-test comparing specific weekdays from before and after the feature to each other, but since there's a trend up, I get a false positive even if no change has been made. So what's the correct approach here? I found this question but am having a hard time understanding the answer, and the series doesn't have the same characteristics as mine (trend, seasonality).
