Forecasting the underlying potential governing the time series of a dynamical system
Livina, VN; Lohmann, G; Mudelsee, M; et al.Lenton, Timothy M.
Date: 15 September 2013
Article
Journal
Physica A: Statistical Mechanics and its Applications
Publisher
Elsevier
Publisher DOI
Abstract
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 ...
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.
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