Time Series Decomposition Using Spring System Applied on Phase Spaces
Felipe S.L.G. Duarte, Ricardo A. Rios, Eduardo R. Hruschka, Rodrigo Fernandes de Mello · 2018
The incremental collection of data streams has motivated their modeling in attempt to take decisions and optimize operations. Most modeling strategies do not take advantage of data decomposition strategies to separate stochastic from deterministic influences and proceed with their individual analyses. Alternatively, one can model them using the most adequate set of tools: Statistical tools to represent stochastic components, and Dynamical systems to address the deterministic ones. Almost all current decomposition strategies impose biases that make data observations lose their deterministic aspects in the phase space, consequently modifying their basins of attraction and compromising recurrent forecasting. This gap motivated us to propose Spring, an unsupervised approach to decompose time series using spring systems over phase spaces, aiming at preserving the attractor topology. Spring was compared against the state-of-the-art techniques (Fourier, Wavelets, SSA, Lazy, and EMD-RP) using synthetic time series (with and without additive noise), confirming that attractor topologies are preserved. In addition, Spring has shown the best results in our experiments, followed by Lazy. All the other assessed approaches failed in nonlinear scenarios.