Multi-Scale Temporal Interpolation Patch Graph Neural Network for Multivariate Time Series Forecasting With Missing Values

Recent studies have revealed the significant potential of spatiotemporal graph neural networks for multivariate time series forecasting with missing values. These methods typically represent interactions between time series as graph structures, where each time step is encoded as a graph node. Existing methods largely rely on self-learned or predefined graph structures to capture spatial dependencies within temporal data. However, in real-world applications, interactions between nodes are often directional and may span long temporal distances. Moreover, at high missing rates, interpolation across time scales often produces varied results in reconstructing missing time series. To address these challenges, this paper investigates the directed interactions of missing values in time series an d their multi-scale interpolation process. We propose the Multi-scale Temporal Interpolation Patch Graph Neural Network (MTIPG), which enables precise spatiotemporal modeling with limited data. Specifically, we first design a hierarchical structure combined with dilated convolutions to capture feature interpolation of missing sequences at specific time scales. Then, we quantify the positional relationships between patches using the dot product similarity between the head and tail embeddings of missing sequences, facilitating implicit modeling of missing variables and directional information propagation. Finally, we integrate these modules to generate accurate prediction results. Extensive experiments on four real-world datasets demonstrate that MTIPG consistently outperforms state-of-the-art baselines across various missing rates, achieving accurate predictions for all variables’ future values, even with up to 60% missing data.