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The reconstruction of phase spaces is an essential step to analyze timeseries according to Dynamical System concepts. A regression performed on suchspaces unveils the relationships among system states from which we can derivetheir generating rules, that is, the most probable set of functions responsiblefor generating observations along time. In this sense, most approaches rely onTakens' embedding theorem to unfold the phase space, which requires theembedding dimension and the time delay. Moreover, although several methods havebeen proposed to empirically estimate those parameters, they still facelimitations due to their lack of consistency and robustness, which hasmotivated this paper. As an alternative, we here propose an artificial neuralnetwork with a forgetting mechanism to implicitly learn the phase spacesproperties, whatever they are. Such network trains on forecasting errors and,after converging, its architecture is used to estimate the embeddingparameters. Experimental results confirm that our approach is either ascompetitive as or better than most state-of-the-art strategies while revealingthe temporal relationship among time-series observations.

Supporting Optimal Phase Space Reconstructions Using Neural Network Architecture for Time Series Modeling