Many complex and important real-life applications, such as surveillance, monitoring and fraud detection, need to identify entire time-series, from a given collection, as anomalous. In this paper, we formulate and propose a solution for this inter-time-series anomaly detection problem, which is different from the usual intra-time-series anomaly detection, which identifies an anomalous “region” within a given single time-series. We formulate the notion of causally anomalous multi-variate time-series, and propose algorithms to identify them in a given database, using well-established notions of both linear and nonlinear Granger causality. The idea is to use (either domain knowledge or frequently observed) causal relations that hold between the univariate time-series corresponding to individual attributes, and identify those time-series as anomalous where this expected causality is violated. We use the proposed algorithms to detect causally anomalous time-series in several public datasets, in different domains such as economics, engineering, and medicine. Our experiments show that the causally anomalous time-series are not detected by strong baseline algorithms, indicating that this is a new notion of anomaly that complements the more standard formulations of what makes a time-series anomalous. We then present a detailed real-life case-study in a large stock exchange, where these techniques were used to identify agents with suspicious order behavior. We also point out limitations of the proposed notion of causally anomalous time-series.
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Apte, M., Vaishampayan, S. & Palshikar, G.K. Detection of causally anomalous time-series. Int J Data Sci Anal 11, 141–153 (2021). https://doi.org/10.1007/s41060-021-00248-2
- Anomaly detection
- Granger causality
- Stock market frauds
- Stock market order book surveillance