MSGNet: Learning Multi-Scale Inter-Series Correlations for Multivariate Time Series Forecasting

TL;DR

MSGNet addresses the challenge of capturing varying inter-series correlations across time scales in multivariate time series forecasting. It jointly learns scale-specific inter-series relationships via adaptive MixHop graph convolution, and intra-series temporal patterns via multi-head attention, with scale identification driven by FFT. The approach demonstrates superior forecasting accuracy and robustness on eight real-world datasets, including out-of-distribution flight data during COVID-19, and provides interpretable multi-scale inter-series graphs. This work advances scale-aware modeling for multivariate forecasting and offers practical gains in accuracy and generalization for complex, real-world systems.

Abstract

Multivariate time series forecasting poses an ongoing challenge across various disciplines. Time series data often exhibit diverse intra-series and inter-series correlations, contributing to intricate and interwoven dependencies that have been the focus of numerous studies. Nevertheless, a significant research gap remains in comprehending the varying inter-series correlations across different time scales among multiple time series, an area that has received limited attention in the literature. To bridge this gap, this paper introduces MSGNet, an advanced deep learning model designed to capture the varying inter-series correlations across multiple time scales using frequency domain analysis and adaptive graph convolution. By leveraging frequency domain analysis, MSGNet effectively extracts salient periodic patterns and decomposes the time series into distinct time scales. The model incorporates a self-attention mechanism to capture intra-series dependencies, while introducing an adaptive mixhop graph convolution layer to autonomously learn diverse inter-series correlations within each time scale. Extensive experiments are conducted on several real-world datasets to showcase the effectiveness of MSGNet. Furthermore, MSGNet possesses the ability to automatically learn explainable multi-scale inter-series correlations, exhibiting strong generalization capabilities even when applied to out-of-distribution samples.

Figures (12)

• Figure 1: In the longer time $\text{scale}_1$, the green and red time series are positively correlated, whereas in the shorter time $\text{scale}_2$, they exhibit a negative correlation. Consequently, we observe two distinct graph structures in these two different time scales.
• Figure 2: MSGNet employs several ScaleGraph blocks, each encompassing three pivotal modules: an FFT module for multi-scale data identification, an adaptive graph convolution module for inter-series correlation learning within a time scale, and a multi-head attention module for intra-series correlation learning.
• Figure 3: Visualization of Flight prediction results: black lines for true values, orange lines for predicted values, and blue markings indicating significant deviations.
• Figure 4: Learned adjacency matrices (24h, 6h, and 4h of the first layer) and airport map for Flight dataset.
• Figure 5: During the onset of the COVID-19 pandemic, there was a drastic decline in the daily flight volume at major airports in Europe, resembling a steep drop-off, which later experienced a gradual recovery.

Theorems & Definitions (3)

• Definition 1
• Theorem 1
• proof