# Online Forecasting and Anomaly Detection Based on the ARIMA Model
## 2 Materials and Methods
### Anomaly Detection Algorithms
#### 2.4.2 One Point Prediction
However, in actual fact, we were able to detect the emergence of an anomaly that has not been detected by existing diagnostic systems, and which ultimately led to serious financial losses. Moreover, this algorithm is an unsupervised change point detection algorithm, which means that it can contribute toward safety, even in the case of previously unknown hidden defects. As for the remaining four hidden defects, there is currently no understanding of whether they impacted the signals from the sensors and, consequently, the possibility of detection. Some more anomaly detection results were obtained using the Numenta Anomaly Benchmark. This benchmark was initially created to evaluate unsupervised real-time anomaly detection algorithms and includes time series data from various sources. The fact that the developed algorithm took third place on the corresponding scoreboard allows us to assert that the developed algorithm can be universally applied. ## 5 Conclusions

Many researchers are working on high-performance anomaly detection and forecasting algorithms with the ability to learn continuously and adapt to changing states. In this paper, we proposed a novel algorithm that can solve all of these challenging tasks simultaneously. It is based on the well-known ARIMA model, which is widely used for

Figure 3: The discrete difference in the modernized ARIMA weight coefficients for turbogenerator-bearing vibration time series. The black vertical line shows the time moment in which the hidden defect arose. time-series modeling. The proposed algorithm works in online mode and uses unlabelled data, making it possible to solve tasks in an unsupervised manner. At the same time, it is much more computationally efficient and almost identically accurate when compared to classical ARIMA-based algorithms. All of these characteristics are essential for online process monitoring, including technical system diagnostics. A library in the Python3 programming language, using the \"ARIMAFD\" algorithm, was also proposed. As such, it is applicable both for anomaly detection and forecasting purposes. For the forecasting problem, the proposed algorithm was compared with two pseudo-online algorithms and the non-learning ARIMA model. The results clearly show that all the algorithms turned out to be quite accurate, while their computational complexity and stability to changes in a system differed significantly, in favor of the developed online ARIMA-based algorithm. The strong ability of the proposed algorithm to find anomalies was confirmed by the fact that it took third place in the Numenta Anomaly Benchmark competition and the fact that it was able to detect a fault in the real-world data from the turbogenerator. The proposed algorithm not only beats the classical ARIMA-based 1-point-ahead prediction (Algorithm 5), but also outperforms most of the well-known online anomaly detection algorithms proposed by respectable researchers. While the results on the NAB prove the applicability of the proposed algorithm in various applications, successful anomaly detection in the turbogenerator data shows the clear benefits that the algorithm can bring in improving the safety and economic efficiency of power plants. Taken together, these results suggest that the combined algorithm we developed may be able to contribute to the development of technical diagnostics and online process monitoring. The next steps in this direction should be the extension of a heuristics list that makes the overall algorithm more robust and invariant to the data, as well as the use of more advanced optimization algorithms. Conceptualization, methodology, software, validation, formal analysis, investigation, resources, data curation, writing--original draft, preparation,visualization, [PERSON] and [PERSON]; writing--review and editing, V.K., I.K. and D.L. ; supervision, D.L. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable.