Time series forecasting is integral to diverse fields, significantly influencing both industrial production and human activities. In the real world, time-series data often exists in the form of streaming data and its distribution often changes over time, which is referred to as concept drift. This results in a gradual decline in the performance of traditional deep learning models as time progresses. Current online learning methods attempt to alleviate this issue by employing online adaptation methods in temporal dimension. However, they overlook the changes and drifts in the inter-variable association within time series. To this end, we propose a novel Online Dynamic Graph Network (ODGNet). ODGNet represents variable associations as a matrix polynomial and acquires polynomial coefficients based on online gradients, which models the evolutionary trends of spatial patterns. Furthermore, we emphasize the lossless information mapping between the adjacency matrix and its corresponding polynomial coefficient. Based on this mapping, a graph memory module with low memory consumption is proposed to avoid catastrophic forgetting when graph drift occurs. And a graph drift awareness mechanism is designed to rapidly detect graph drift. Experimental results demonstrate that ODGNet achieves a significant reduction in forecasting error compared to the existing online learning methods on twelve benchmark datasets. The code is available at https://github.com/LiuYasuo/ODGNet.

Multivariate time series forecasting is crucial across various industries, where accurate extraction of complex periodic and trend components can significantly enhance prediction performance. However, existing models often struggle to capture these intricate patterns. To address these challenges, we propose FilterTS, a novel forecasting model that utilizes specialized filtering techniques based on the frequency domain. FilterTS introduces a Dynamic Cross-Variable Filtering Module, a key innovation that dynamically leverages other variables as filters to extract and reinforce shared variable frequency components across variables in multivariate time series. Additionally, a Static Global Filtering Module captures stable frequency components, identified throughout the entire training set. Moreover, the model is built in the frequency domain, converting time-domain convolutions into frequency-domain multiplicative operations to enhance computational efficiency. Extensive experimental results on eight real-world datasets have demonstrated that FilterTS significantly outperforms existing methods in terms of prediction accuracy and computational efficiency.