Graph Convolution Recurrent Denoising Diffusion Model for Multivariate Probabilistic Temporal Forecasting

The probabilistic estimation for multivariate time series forecasting has recently become a trend in various research fields, such as traffic, climate, and finance. The multivariate time series can be treated as an interrelated system, and it is significant to assume each variable to be independent. However, most existing methods fail to simultaneously consider spatial dependencies and probabilistic temporal dynamics. To address this gap, we introduce the Graph Convolution Recurrent Denoising Diffusion model (GCRDD), a recurrent framework for spatial-temporal forecasting that captures both spatial dependencies and temporal dynamics. Specifically, GCRDD incorporates the structural dependency into a hidden state using the graph-modified gated recurrent unit and samples from the estimated data distribution at each time step by a graph conditional diffusion model. We reveal the comparative experiment performance of state-of-the-art models in two real-world road network traffic datasets to demonstrate it as the competitive probabilistic multivariate temporal forecasting framework.