How do I select data going back a period of time for each group?

I want for each group id to get the latest week's worth of data. Not from a specific date, but counting backwards from the MAX(startTime) of each individual group.

However, the following does not seem to work. I assume it's because startTime in each group (a single value) is BETWEENed by itself? Otherwise, how do I keep it in my filter?

SELECT
    id
  , startTime
FROM MyTable
GROUP BY id, startTime
HAVING startTime BETWEEN MAX(startTime) - INTERVAL 1 WEEK AND MAX(startTime)

What's the right query?

Also, in my case it has to work with MySQL 5.7.

SELECT m.id, m.startTime
FROM (
 SELECT id, MAX(startTime) AS startTime 
 FROM MyTable GROUP BY id
) AS x
JOIN MyTable AS m ON m.id = x.id
 AND m.startTime BETWEEN x.startTime - INTERVAL 1 WEEK AND x.startTime;