Didier Sornette is an econophysicist who models complex events ranging from earthquakes to financial collapses. In a recent publication at arXiv (pdf), he and his team came within a week of predicting the correct date for the collapse of the Chinese equity markets. The paper is a little shy of details on the methods used, and the date wasn't exactly right, but the Swiss team gets points for daring a very near term prediction that could have been completely off-base.
Also interesting material for further reading, Sornette proposes the term "dragon-king" (pdf) for a meaningful outlier that represents a bifurcation or phase change resulting from self-organizational characteristics of open, complex systems, and relates these to the Black Swan concept. Elsewhere, John Robb notes the connection to Ilya Prigogine's Dissipative Structures.