CCD: Capturing Cross-Correlations with Deformable Convolutional Networks for Multivariate Time Series Forecasting

The accuracy of Multivariate Time Series Forecasting relies on capturing precise channel correlations. Recent studies have primarily focused on capturing distinct channel relationships within each individual frequency and scale. However, complex channel dependencies are more prominently found in correlations across scales and frequencies. We term these relationships as Cross-Correlations. Drawing inspiration from Computer Vision, an efficient and effective strategy for capturing such 2D dependencies is to represent time series as Channel-Frequency and Channel-Scale views that possess image-like structures, and then use Convolutional Neural Networks to capture these complex Cross-Correlations. However, it is challenging to capture Cross-Correlations as the correlated parts are often non-local distributed in the views. For this challenge, we propose the Adaptive 2-Dimensional Shuffle that permutes the rows and columns of the Channel-Frequency and Channel-Scale views before applying CNNs. Nevertheless, these views still lack well-defined spatial properties. To address this challenge, we further propose a novel Cross Deformable Convolution. In this module, we design a more data-adaptive kernel shape with enhanced robustness and scalability, and introduce a dynamic sparse interaction mechanism to effectively capture complex Cross-Correlations. In summary, we propose a novel framework called CCD, which Captures Cross-Correlations with Deformable Convolutional Networks for Multivariate Time Series Forecasting. Extensive experiments on real-world datasets demonstrate the state-of-the-art performance of CCD.