Supporting Optimal Phase Space Reconstructions Using Neural Network Architecture for Time Series Modeling
This addresses a limitation in dynamical systems analysis for researchers and practitioners dealing with time series data, though it appears incremental as it builds on existing methods.
The paper tackles the challenge of consistently and robustly estimating embedding parameters for phase space reconstruction in time series analysis by proposing a neural network with a forgetting mechanism that learns phase space properties from forecasting errors. Experimental results show the approach is competitive with or better than most state-of-the-art strategies.
The reconstruction of phase spaces is an essential step to analyze time series according to Dynamical System concepts. A regression performed on such spaces unveils the relationships among system states from which we can derive their generating rules, that is, the most probable set of functions responsible for generating observations along time. In this sense, most approaches rely on Takens' embedding theorem to unfold the phase space, which requires the embedding dimension and the time delay. Moreover, although several methods have been proposed to empirically estimate those parameters, they still face limitations due to their lack of consistency and robustness, which has motivated this paper. As an alternative, we here propose an artificial neural network with a forgetting mechanism to implicitly learn the phase spaces properties, whatever they are. Such network trains on forecasting errors and, after converging, its architecture is used to estimate the embedding parameters. Experimental results confirm that our approach is either as competitive as or better than most state-of-the-art strategies while revealing the temporal relationship among time-series observations.