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The forecasting of multi-variate time processes through graph-basedtechniques has recently been addressed under the graph signal processingframework. However, problems in the representation and the processing arisewhen each time series carries a vector of quantities rather than a scalar one.To tackle this issue, we devise a new framework and propose new methodologiesbased on the graph vector autoregressive model. More explicitly, we leverageproduct graphs to model the high-dimensional graph data and developmulti-dimensional graph-based vector autoregressive models to forecast futuretrends with a number of parameters that is independent of the number of timeseries and a linear computational complexity. Numerical results demonstratingthe prediction of moving point clouds corroborate our findings.

Forecasting Multi-Dimensional Processes over Graphs