How to predict the duration of burst given several series
I guess, a nice place to start is seminal work of John Kleinberg:  https://www.cs.cornell.edu/home/kleinber/bhs.pdf
Yes, this paper is outdated, but anyway it's still very influential and simple. Also, digging articles, citing this paper, could be very helpful. By the way, these guys solve very similar task ( and they even use Weibo logs as well!): http://www.csce.uark.edu/~xintaowu/publ/pakdd15.pdf