Detecting anomalies in data streams driven by ajump-diffusion process

Abstract: Jump-diffusion processes often model financial time series as they can simulate the random jumps that they frequently exhibit. These jumps can be seen as anomalies and are essential for financial analysis and model building, making them vital to detect.The realized variation, realized bipower variation, and realized semi-variation were tested to see if one could use them to detect jumps in a jump-diffusion process and if anomaly detection algorithms can use them as features to improve their accuracy. The algorithms tested were Isolation Forest, Robust Random Cut Forest, and Isolation Forest Algorithm for Streaming Data, where the latter two use streaming data. This was done by generating a Merton jump-diffusion process with a varying jump-rate and tested using each algorithm with each of the features. The performance of each algorithm was measured using the F1-score to compare the difference between features and algorithms. It was found that the algorithms were improved from using the features; Isolation Forest saw improvement from using one, or more, of the named features. For the streaming algorithms, Robust Random Cut Forest performed the best for every jump-rate except the lowest. Using a combination of the features gave the highest F1-score for both streaming algorithms. These results show one can use these features to extract jumps, as anomaly scores, and improve the accuracy of the algorithms, both in a batch and stream setting.