MGCP: A Multi-Grained Correlation based Prediction Network for Multivariate Time Series

TL;DR

MGCP tackles multivariate time series forecasting by explicitly modeling correlations at fine-, medium-, and coarse-grained levels. It integrates Adaptive Fourier Neural Operators for global spatiotemporal patterns, Graph Convolutional Networks for inter-series relations, and a Transformer-based predictor with a conditional Wasserstein GAN discriminator to align forecasts with the true distribution. Across real-world datasets, MGCP achieves state-of-the-art performance without requiring predefined graph structures, and ablations confirm the essential roles of AFNO, GCN, and adversarial training. This approach advances robust, distribution-aware forecasting for complex, multi-variate data across diverse domains.

Abstract

Multivariate time series prediction is widely used in daily life, which poses significant challenges due to the complex correlations that exist at multi-grained levels. Unfortunately, the majority of current time series prediction models fail to simultaneously learn the correlations of multivariate time series at multi-grained levels, resulting in suboptimal performance. To address this, we propose a Multi-Grained Correlations-based Prediction (MGCP) Network, which simultaneously considers the correlations at three granularity levels to enhance prediction performance. Specifically, MGCP utilizes Adaptive Fourier Neural Operators and Graph Convolutional Networks to learn the global spatiotemporal correlations and inter-series correlations, enabling the extraction of potential features from multivariate time series at fine-grained and medium-grained levels. Additionally, MGCP employs adversarial training with an attention mechanism-based predictor and conditional discriminator to optimize prediction results at coarse-grained level, ensuring high fidelity between the generated forecast results and the actual data distribution. Finally, we compare MGCP with several state-of-the-art time series prediction algorithms on real-world benchmark datasets, and our results demonstrate the generality and effectiveness of the proposed model.

Figures (7)

• Figure 1: Exploring Correlations Patterns of Multivariate Time Series at Multi-Grained Levels: Examples and Illustrations. This figure showcases the correlations of multivariate time series at fine-grained, medium-grained and coarse-grained levels using three time series, each with four timestamps, as examples. At fine-grained level, Panel (a) displays the correlations between different timestamps in each time series, i.e. the temporal correlations, Panel (b) illustrates the correlations between different time series at a certain timestamp, i.e., the cross-sectional correlations and Panel (c) highlights the correlations between arbitrary timestamps for any time series, which we define as the global spatiotemporal correlations. At medium-grained level, Panel (d) shows the correlations between different time series, i.e., inter-series correlations. At coarse-grained level, Panel (e) shows the overall properties of multivariate time series, including whether it follows or approaches a distribution $p$, which may be a conditional distribution in the forecasting task.
• Figure 2: Workflow of Multi-Grained Correlations-based Prediction Network. The latent space mapper mainly includes Masked AFNO and GCN, as shown in Fig. \ref{['fig:mapper']}. Both the sequence predictor and the conditional discriminator is composed of an attention-based encoder and an attention-based decoder. The restoration component consists of the AFNO and multi-layer fully connected networks.
• Figure 3: The structure of the latent space mapper.
• Figure 4: Evaluation of the performance with respect to varied $\gamma$ over partial datasets. The blue dots represent the average test error over multiple experiments, and the black lines represent the corresponding variances.
• Figure 5: How training loss vary with epochs under different $\lambda$.