# Multivariate Time Series Deep Spatiotemporal Forecasting with Graph Neural Network
## 1 Introduction  
With the development of the Internet, various sensors and data-storage devices have appeared in modern society. As a result, a large amount of time series data is generated by recording temperature, traffic, power consumption, and financial data. Multivariate time series data consists of time series data generated by multiple sensors or data storage devices, and there are dependencies among multiple time series. For example, a household's daily electricity usage and hourly electricity production from solar panels can be considered time series data. In most cases, the data usually come from the electricity consumed by multiple households or solar data generated at different locations. A multivariate time series is constructed from these data. There may be complex dynamic dependencies between multivariate time series data. Therefore, each time series in a multivariate time series is helpful for forecasting tasks. At the same time, multivariate time series data such as electricity and transportation have periodic characteristics. Multivariate time series forecasting has been studied for a long time in capturing the periodic characteristics and dynamic dependencies of variables [1; 2; 3; 4]. For example, studies using the Harmonicregression method enhanced the prediction performance of PM\({}_{2.5}\) by capturing periodic information [5]. In recent years, some researchers have made efforts in time series analysis and forecasting. For example, traditional forecasting methods represented by statistical methods. Most rely on mathematical equations to describe the evolution of time series, such as the Autoregressive Integrated Moving Average Model (ARIMA) [6]. Therefore, various variants based on the ARIMA model have emerged. Models based on traditional methods are more computationally efficient. However, these models are mostly limited to linear models and univariate predictions. It is difficult to extend to multivariate time series problems. In the era of big data, with the development of sensor technology and computing power, most of the time series data comes from data collected by various devices. However, the information of large-scale data is difficult to extract by traditional methods. Deep learning is the current popular information extraction method. Features of large-scale data can be obtained through deep learning techniques. In time series forecasting, deep learning techniques are employed to achieve better forecasting accuracy than traditional methods. At the same time, deep learning technology has made great progress in the research and application of image processing, audio processing and natural language processing [7; 8; 9]. Although traditional machine learning and statistical methods are often employed in time series forecasting tasks, deep learning techniques are gaining attention from researchers. With further development, there have been studies on applying graph neural networks and attention methods in time series forecasting [10; 11; 12]. Capturing spatial information by building a graph structure of multivariate time series. These methods have achieved certain results. A graph neural network allows each node in the graph to acquire information about the surrounding nodes. Multivariate time series can be considered from the perspective of graph nodes. Spatial information can be obtained between multivariate time series by constructing graphs. For periodic data, the information of adjacent nodes is more informative. Compared with vanilla neural networks, graph neural networks can capture the dependency information between different sequences, which is more suitable for the prediction of multivariate time series. Therefore, graph neural networks can achieve more accurate prediction results than vanilla neural networks by aggregating information from multiple sequences. In this paper, a multivariate time series deep spatiotemporal forecasting model with a graph neural network (MDST-GNN) is proposed.