atlantic87 - 6:06 am on Oct 19, 2013 (gmt 0)
I have had this for the past 2 weeks or so. At first the visits were for a main keyword (and StatCounter reported that the SERP position was #1 -- even though I usually rank on page 2 for that keyword), but for the past week the keyword has just been my site's URL.
The visits are always just of the homepage, and are always around the same time, 11:00 pm. Very strange.