If you aren't getting any alerts from avast, then I'm afraid there won't be anything recorded to whatever log (shield log) the activity was recorded in.
The first issue is identifying what shield might be involved, this is most likely to be the file system shield and the web shield. You would effectively have to set those shields log settings (Report file) to record, Soft errors, OK items and Skipped items.
There is a downside to this as the file would get big pretty quick.