Decomposing time series into deterministic and stochastic influences: A survey

Temporal data produced by industrial, human, and natural phenomena typically contain deterministic and stochastic influences, being the first ideally modelled using Dynamical Systems while the second is appropriately addressed using Statistical tools. Although such influences have been widely studied as individual components, specific tools are required to support their decomposition for a proper modeling and analysis. This article addresses a comprehensive survey of the main time-series decomposition strategies and their relative performances in different application domains. The following strategies are discussed: i) Fourier Transform, ii) Wavelet transforms, iii) Moving Average, iv) Singular Spectrum Analysis, v) Lazy, vi) GHKSS, and vii) other approaches based on the Empirical Mode Decomposition method. In order to assess these strategies, we employ diverse and complementary performance measures: i) Mean Absolute Error, Mean Squared and Root Mean Squared Errors; ii) Minkowski Distances; iii) Complexity-Invariant Distance; iv) Pearson correlation; v) Mean Distance from the Diagonal Line; and vi) Mean Distance from Attractors. Each decomposition strategy is better devoted to particular scenarios, however, without any previous knowledge on data, GHKSS confirmed to work as a fair and general baseline besides its time complexity.