{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/data-driven-detrending-of-nonstationary","title":"Data-driven detrending of nonstationary fractal time series with echo state networks","arxiv_id":"1510.07146","date":"2015-10-24","proceeding":null,"authors":["Enrico Maiorino","Filippo Maria Bianchi","Lorenzo Livi","Antonello Rizzi","Alireza Sadeghian"],"abstract":"In this paper, we propose a novel data-driven approach for removing trends\n(detrending) from nonstationary, fractal and multifractal time series. We\nconsider real-valued time series relative to measurements of an underlying\ndynamical system that evolves through time. We assume that such a dynamical\nprocess is predictable to a certain degree by means of a class of recurrent\nnetworks called Echo State Network (ESN), which are capable to model a generic\ndynamical process. In order to isolate the superimposed (multi)fractal\ncomponent of interest, we define a data-driven filter by leveraging on the ESN\nprediction capability to identify the trend component of a given input time\nseries. Specifically, the (estimated) trend is removed from the original time\nseries and the residual signal is analyzed with the multifractal detrended\nfluctuation analysis procedure to verify the correctness of the detrending\nprocedure. In order to demonstrate the effectiveness of the proposed technique,\nwe consider several synthetic time series consisting of different types of\ntrends and fractal noise components with known characteristics. We also process\na real-world dataset, the sunspot time series, which is well-known for its\nmultifractal features and has recently gained attention in the complex systems\nfield. Results demonstrate the validity and generality of the proposed\ndetrending method based on ESNs.","url_abs":"http://arxiv.org/abs/1510.07146v2","url_pdf":"http://arxiv.org/pdf/1510.07146v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"data-driven-detrending-of-nonstationary","repo_url":"https://bitbucket.org/slackericida/desn_v1","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}