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

TL;DR

This paper introduces a novel potential forecasting method that uses polynomial approximation of probability distributions to predict future states of dynamical systems, demonstrated on climate and Arctic sea-ice data.

Contribution

The paper presents a new general framework for potential analysis of time series, enabling anticipation and detection of non-linear changes and bifurcations.

Findings

Successfully forecasted artificial and climate data

Applied to Arctic sea-ice time series for future prediction

Framework integrates multiple techniques for non-linear change detection

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 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 non-linear 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.