The challenge of effectively learning inter-series correlations for
multivariate time series forecasting remains a substantial and unresolved
problem. Traditional deep learning models, which are largely dependent on the
Transformer paradigm for modeling long sequences, often fail to integrate
information from multiple time series into a coherent and universally
applicable model. To bridge this gap, our paper presents ForecastGrapher, a
framework reconceptualizes multivariate time series forecasting as a node
regression task, providing a unique avenue for capturing the intricate temporal
dynamics and inter-series correlations. Our approach is underpinned by three
pivotal steps: firstly, generating custom node embeddings to reflect the
temporal variations within each series; secondly, constructing an adaptive
adjacency matrix to encode the inter-series correlations; and thirdly,
augmenting the GNNs' expressive power by diversifying the node feature
distribution. To enhance this expressive power, we introduce the Group Feature
Convolution GNN (GFC-GNN). This model employs a learnable scaler to segment
node features into multiple groups and applies one-dimensional convolutions
with different kernel lengths to each group prior to the aggregation phase.
Consequently, the GFC-GNN method enriches the diversity of node feature
distribution in a fully end-to-end fashion. Through extensive experiments and
ablation studies, we show that ForecastGrapher surpasses strong baselines and
leading published techniques in the domain of multivariate time series
forecasting.

ForecastGrapher 是一个框架，将多变量时间序列预测重新构想为节点回归任务，通过生成自定义节点嵌入、构建自适应邻接矩阵和增强节点特征分布的表达能力，引入 GFC-GNN 模型来捕捉复杂的时间动态和跨序列的相关性，通过大量实验证明其在多变量时间序列预测领域超过了强基线和领先的已发表技术。

ForecastGrapher：用图神经网络重新定义多元时间序列预测

ForecastGrapher: Redefining Multivariate Time Series Forecasting with  Graph Neural Networks

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.

本文介绍了 MSGNet，一种先进的深度学习模型，通过频域分析和自适应图卷积来捕捉多个时间尺度下不同时间序列之间变化的相互关系，进一步展示了 MSGNet 学习可解释的多尺度时间序列间相互关系的自动能力。

MSGNet：学习多尺度跨序列相关性用于多元时间序列预测

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

Multivariate time-series forecasting plays a crucial role in many real-world
applications. It is a challenging problem as one needs to consider both
intra-series temporal correlations and inter-series correlations
simultaneously. Recently, there have been multiple works trying to capture both
correlations, but most, if not all of them only capture temporal correlations
in the time domain and resort to pre-defined priors as inter-series
relationships.
In this paper, we propose Spectral Temporal Graph Neural Network (StemGNN) to
further improve the accuracy of multivariate time-series forecasting. StemGNN
captures inter-series correlations and temporal dependencies \textit{jointly}
in the \textit{spectral domain}. It combines Graph Fourier Transform (GFT)
which models inter-series correlations and Discrete Fourier Transform (DFT)
which models temporal dependencies in an end-to-end framework. After passing
through GFT and DFT, the spectral representations hold clear patterns and can
be predicted effectively by convolution and sequential learning modules.
Moreover, StemGNN learns inter-series correlations automatically from the data
without using pre-defined priors. We conduct extensive experiments on ten
real-world datasets to demonstrate the effectiveness of StemGNN. Code is
available at this https URL

本篇论文提出了一种 Spectral Temporal Graph Neural Network (StemGNN) 模型，通过 Graph Fourier Transform （GFT）和 Discrete Fourier Transform（DFT）相结合的方法，同时捕获了时间序列内部的时间相关性和时间序列间的相关性，在预测方面具有良好的性能。此外，该模型在不使用预定义先验的情况下自动地学习序列间的相关性。