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

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