Self-paced ARIMA for robust time series prediction

For time series prediction tasks, the autoregressive integrated moving average (ARIMA) model is one of the most classical and popular linear models, and extended applications have achieved satisfying prediction accuracy in many domains. However, less work has focused on the influence of noisy data, which causes the instability of ARIMA and a sharp decline in performance. In this paper, we propose a robust time series prediction framework named spARIMA. To reduce noise interference in the training process, we design a sequential training scheme in batches based on the degree of noise and the contribution to the correct modeling. spARIMA relies on the differential prediction model in ARIMA and absorbs the advantages of the gradual training scheme in self-paced learning (SPL) so that spARIMA can effectively address the instability caused by noise. Moreover, considering that the similarity of selected samples may generate local optimal solutions, we extend spARIMA to diversity selection, which utilizes a weighted local complexity-similarity distance expression to represent the diversity of noisy data. We test the performance of spARIMA on twelve datasets compared with existing ARIMA models on two gradient descent algorithms. The results show that our method is not only suitable for noisy data but also efficient for normal data, which indicates the generalization ability of spARIMA.(c) 2023 Elsevier B.V. All rights reserved.

Automated summary

This paper proposes a robust time series prediction framework called spARIMA, which reduces noise interference by designing a sequential training scheme in batches based on the degree of noise. spARIMA relies on the differential prediction model in ARIMA and absorbs the advantages of the gradual training scheme in self-paced learning (SPL) to effectively address the instability caused by noise. Furthermore, spARIMA introduces diversity selection to avoid selecting similar samples, using a weighted local complexity-similarity distance expression to represent the diversity of noisy data. Comparative tests with existing ARIMA models on two gradient descent algorithms show that spARIMA not only works well with noisy data, but also performs efficiently with normal data, indicating its generalization ability.