Working out when something you are seeing is not something you should have been expecting, in some sense which will not be made rigorous here, not yet.
Nuit Blanche has a roundup.
Henrickson, Scott, Jeff Kolb, Brian Lehmann, and Joshua Montague. 2015. “Trend Detection in Social Data.” Twitter. https://github.com/jeffakolb/Gnip-Trend-Detection.
Kandanaarachchi, Sevvandi, Mario A. Munoz, Rob J. Hyndman, and Kate Smith-Miles. 2018. “On Normalization and Algorithm Selection for Unsupervised Outlier Detection.” 16/18. Monash Econometrics and Business Statistics Working Papers. Monash University, Department of Econometrics and Business Statistics. https://www.monash.edu/business/ebs/research/publications/ebs/wp16-2018.pdf.
Lopez, Jose A., Octavia Camps, and Mario Sznaier. 2015. “Robust Anomaly Detection Using Semidefinite Programming,” April. http://arxiv.org/abs/1504.00905.
Nikolov, Stanislav. 2012. “Trend or No Trend : A Novel Nonparametric Method for Classifying Time Series.” Thesis, Massachusetts Institute of Technology. http://dspace.mit.edu/handle/1721.1/85399.
She, Yiyuan, and Art B. Owen. 2010. “Outlier Detection Using Nonconvex Penalized Regression.” http://statweb.stanford.edu/~owen/reports/theta-ipod.pdf.