Ask HN: Does retargeting hit the wrong consumers?

I'm doing some research on a company that spends a large amount of money on banner advertising. Some of their data suggest a relationship between sales and ads displayed in the days or weeks AFTER those sales were made. That made me wonder - is it likely that banner display networks, especially ones that use retargeting, are serving impressions to users after they've already made a purchasing decision, especially in the case of high-dollar purchases? I don't have enough data to effectively answer that question, but based on the relationships I'm seeing as well as some anecdotal experience, I think there's a strong possibility that this is the case. Have any of you seen data that supports or opposes a similar conclusion?