This paper presents a novel learning methodology for multigrid-based fuzzy system (MGFS), and its application to the CATS time series prediction benchmark. The MGFS model keeps the advantages of the traditional grid-based fuzzy systems (GBFS), and overcomes the problem inherent to all GBFSs when dealing with high dimensional input data. Thus the MGFS model keeps interpretability, low computational cost and high generalization. A novel architecture selection algorithm for MGFSs that allows performing input variable selection is proposed. It identifies the sub-optimal architecture, according to a provided data set of input/output data. The architecture selection algorithm is completed with a structure identification procedure, used to obtain the optimal input space partitioning of the different sub-grids of the model. The complete algorithm is used to obtain the MGFS models for the CATS series prediction problem, solved using a direct prediction-based approach.