Decomposition of Dynamical Signals into Jumps, Oscillatory Patterns, and Possible Outliers

Elena Barton (1) , Basad Al-Sarray (2) , Stephane Chretien (3, 1) , Kavya Jagan (1)

1 NPL - National Physical Laboratory [Teddington]
2 University of Baghdad
3 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

In this note, we present a component-wise algorithm combining several recent ideas from signal processing for simultaneous piecewise constants trend, seasonality, outliers, and noise decomposition of dynamical time series. Our approach is entirely based on convex optimisation, and our decomposition is guaranteed to be a global optimiser. We demonstrate the efficiency of the approach via simulations results and real data analysis.

Mots clés: trend filtering; time series; dynamical systems; robust principal component analysis (PCA); outlier extraction; Prony's method

Domaines: Statistiques [math.ST]; Machine Learning [stat.ML]

Elena Barton, Basad Al-Sarray, Stephane Chretien, Kavya Jagan. Decomposition of Dynamical Signals into Jumps, Oscillatory Patterns, and Possible Outliers. Mathematics , 2018, 6 (7), pp.124. ⟨10.3390/math6070124⟩. ⟨hal-02515951⟩