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

TL;DR

This paper introduces a neural network-based method with a forgetting mechanism to implicitly learn phase space properties for time series analysis, improving the estimation of embedding parameters over traditional methods.

Contribution

The proposed neural network approach offers a robust, data-driven alternative to traditional parameter estimation methods for phase space reconstruction in time series analysis.

Findings

Competitive with state-of-the-art strategies

Reveals temporal relationships among observations

Improves robustness and consistency in parameter estimation

Abstract

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.