1 research outputs found
Supporting Optimal Phase Space Reconstructions Using Neural Network Architecture for Time Series Modeling
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.Comment: 13 pages (16 including references), 12 figure