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.
Special case: “trend detection”. e.g. Gnip Trend detection [Niko12] looks fun, and comes with a cute explanation of how you might do this nonparametrically.
- Kand00: (n.d.) Kandanaarachchi et al - 2018 - On normalization and algorithm selection for unsup.pdf.
- KMHS18: (2018) On normalization and algorithm selection for unsupervised outlier detection (No. 16/18) (p. 34). Monash University, Department of Econometrics and Business Statistics
- ShOw10: (2010) Outlier Detection Using Nonconvex Penalized Regression.
- LoCS15: (2015) Robust Anomaly Detection Using Semidefinite Programming. ArXiv:1504.00905 [Cs, Math].
- HKLM15: (2015) Trend detection in social data. Twitter
- Niko12: (2012) Trend or no trend : a novel nonparametric method for classifying time series (Thesis). Massachusetts Institute of Technology