Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks

Abstract

Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its variables depend on one another but, upon looking closely, it is fair to say that existing methods fail to fully exploit latent spatial dependencies between pairs of variables. In recent years, meanwhile, graph neural networks (GNNs) have shown high capability in handling relational dependencies. GNNs require well-defined graph structures for information propagation which means they cannot be applied directly for multivariate time series where the dependencies are not known in advance. In this paper, we propose a general graph neural network framework designed specifically for multivariate time series data. Our approach automatically extracts the uni-directed relations among variables through a graph learning module, into which external knowledge like variable attributes can be easily integrated. A novel mix-hop propagation layer and a dilated inception layer are further proposed to capture the spatial and temporal dependencies within the time series. The graph learning, graph convolution, and temporal convolution modules are jointly learned in an end-to-end framework. Experimental results show that our proposed model outperforms the state-of-the-art baseline methods on 3 of 4 benchmark datasets and achieves on-par performance with other approaches on two traffic datasets which provide extra structural information. CCS CONCEPTS• Computing methodologies → Neural networks; Artificial intelligence.

Adaptively temporal graph convolution model for epidemic prediction of multiple age groups

“…If the model can automatically extract the contact pattern among multiple age groups, the latent dependencies of multivariate time series can be combined to improve the prediction. Our study adopts the adaptive graph learning module [29] , which is illustrated as follows: where represent randomly initialized node embeddings, which are learnable during training; are model parameters; is a hyper-parameter for controlling the saturation rate of the activation function. The adaptive graph learning module measures the similarity between the embeddings of each node and computes the matrix A of the directed graph .…”

“…There are also several studies that use GNN to integrate population migration data for infectious disease prediction 25 , 26 , 27 , 28 . Different from RNNs, multivariate time series are processed in a graph structure in GNN, so the independence of time series can be defined by interaction weights and be learned in a data-driven way [29] .…”

HIFI: Anomaly Detection for Multivariate Time Series with High-order Feature Interactions

“…Inspired by MTGNN [11], we directly transform the original features X = (x t−w+1 , x t−w+2 , • • • , x t ) ∈ R w×d to the hidden space…”

Time Series Forecasting of Univariate Agrometeorological Data: A Comparative Performance Evaluation via One-Step and Multi-Step Ahead Forecasting Strategies

“…For this, the authors proposed a transformation-gated LSTM (TG-LSTM) and compared the model performance against nine different recurrent and attention-based models. In the recent times, Graph Neural Networks (GNNs) have gained popularity in multivariate time series forecasting where temporal and latent interdependencies between variables can be represented using graphs with nodes as variables and edges representing the dependencies between variables [ 31 , 32 ]. Unarguably generating ahead-of-time forecasts for financial time series is one of the most challenging and widely studied problems in the domain of time series forecasting.…”