Evaluating Methods for Detrending Time Series Using Ordinal Patterns, with an Application to Air Transport Delays

Abstract

Functional networks have become a standard tool for the analysis of complex systems, allowing the unveiling of their internal connectivity structure while only requiring the observation of the system’s constituent dynamics. To obtain reliable results, one (often overlooked) prerequisite involves the stationarity of an analyzed time series, without which spurious functional connections may emerge. Here, we show how ordinal patterns and metrics derived from them can be used to assess the effectiveness of detrending methods. We apply this approach to data representing the evolution of delays in major European and US airports, and to synthetic versions of the same, obtaining operational conclusions about how these propagate in the two systems.

Keywords

• time series
• stationarity
• functional complex networks
• ordinal patterns
• causality