Data-driven detrending of nonstationary fractal time series with echo state networks

摘要: Abstract In this paper, we propose a novel data-driven approach for removing trends (detrending) from nonstationary, fractal and multifractal time series. We consider real-valued series relative to measurements of an underlying dynamical system that evolves through time. assume such process is predictable certain degree by means class recurrent networks called Echo State Network (ESN), which are capable model generic process. order isolate the superimposed (multi)fractal component interest, define filter leveraging on ESN prediction capability identify trend given input Specifically, (estimated) removed original residual signal analyzed with detrended fluctuation analysis procedure verify correctness detrending procedure. demonstrate effectiveness proposed technique, several synthetic consisting different types noise components known characteristics. also real-world dataset, sunspot series, well-known its features has recently gained attention in complex systems field. Results validity generality method based ESNs.