Reddit mentions of An Introduction to Statistical Modeling of Extreme Values

In some sense you have a form of rare-events happening and thus your "outliers" could probably be modelled using standard Extreme Value Theory - you fit your overall trend in some standard way, and then the extreme residuals have some distribution (that you can e.g. fit parameters to). In some sense what you want to do depends o what you want to do though. If you have a library handy you might consider skimming through a book such as this: http://www.amazon.com/Introduction-Statistical-Modeling-Extreme-Values/dp/1852334592 .