Abstract:Forecasting of multivariate time-series is an important problem that has applications in many domains, including traffic management, cellular network configuration, and quantitative finance. In recent years, researchers have demonstrated the value of applying deep learning architectures for these problems. A special case of the problem arises when there is a graph available that captures the relationships between the time-series. In this paper we propose a novel learning architecture that achieves performance competitive with or better than the best existing algorithms, without requiring knowledge of the graph. The key elements of our proposed architecture are (i) jointly performing backcasting and forecasting with a deep fully-connected architecture; (ii) stacking multiple prediction modules that target successive residuals; and (iii) learning a separate causal relationship graph for each layer of the stack. We can view each layer as predicting a component of the time-series; the differing nature of the causal graphs at different layers can be interpreted as indicating that the multivariate predictive relationships differ for different components. Experimental results for two public traffic network datasets illustrate the value of our approach, and ablation studies confirm the importance of each element of the architecture.