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

Elena Barton, Basad Al-Sarray, Stéphane Chrétien and Kavya Jagan
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Elena Barton: National Physical Laboratory, Teddington, Middlesex TW11 0LW, UK
Basad Al-Sarray: Department of Computer Science, College of Science, University of Baghdad, Aljadirya, Baghdad 10071, Iraq
Stéphane Chrétien: National Physical Laboratory, Teddington, Middlesex TW11 0LW, UK
Kavya Jagan: National Physical Laboratory, Teddington, Middlesex TW11 0LW, UK

Mathematics, 2018, vol. 6, issue 7, 1-13

Abstract: 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.

Keywords: dynamical systems; time series; trend filtering; robust principal component analysis (PCA); outlier extraction; Prony’s method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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