A group called New World Hackers have claimed responsibility[1]. I read a bit that they stopped their attacks by 2pm EST, and that another group picked up some of the minor attacks later in the day. Anonymous was mentioned, but didn't claim it. I can't seem to track down that article at the moment... I'll keep looking.

[1] https://twitter.com/fbajak/status/789611472280178688 and http://www.anonintelgroup.com/2016/10/21/twitter-down-its-no...