Forecasting time series on graphs is a fundamental problem in graph signal processing. When each entity of the network carries a vector of values for each time stamp instead of a scalar one, existing approaches resort to the use of product graphs to combine this multidimensional information, at the expense of creating a larger graph. In this paper, we show the limitations of such approaches, and propose extensions to tackle them. Then, we propose a recursive multiple-input multiple-output graph filter which encompasses many already existing models in the literature while being more flexible. Numerical simulations on a real world data set show the effectiveness of the proposed models.