Forecasting the underlying potential governing the time series of a dynamical system

• Published in: Physica A: Statistical Mechanics and its Applications
• Main Authors: Livina, VN, Lohmann, G, Mudelsee, M, Lenton, Timothy M.
• Format: Article in Journal/Newspaper
• Language: English
• Published: Elsevier 2013
• Subjects: Potential forecasting; Potential analysis; Time series analysis; Arctic; Sea ice
• Online Access: http://hdl.handle.net/10871/15093; https://doi.org/10.1016/j.physa.2013.04.036

Copyright © 2013 The Authors. Published by Elsevier B.V. All rights reserved. We introduce a technique of time series analysis, potential forecasting, which is based on dynamical propagation of the probability density of time series. We employ polynomial coefficients of the orthogonal approximation of the empirical probability distribution and extrapolate them in order to forecast the future probability distribution of data. The method is tested on artificial data, used for hindcasting observed climate data, and then applied to forecast Arctic sea-ice time series. The proposed methodology completes a framework for ‘potential analysis’ of tipping points which altogether serves anticipating, detecting and forecasting nonlinear changes including bifurcations using several independent techniques of time series analysis. Although being applied to climatological series in the present paper, the method is very general and can be used to forecast dynamics in time series of any origin. NERC AXA Research Fund European Commission