I've got sets of time series data collected from Weibo. It contains the number of posts under certain topics over a year. It can be found that from time to time there're bursts of discussion on certain topic. What's interesting is some burst die down quickly while others sustain on the agenda for quite a long time and die down gradually. How to predict and model the decays given a time series data. Also, I've got data of some exogenous data including time series data of links, pictures, and retweeting and original data in the community. Can I predict the duration of decay from these variables?