Generalized Symbolic Dynamics Weighted Network Prediction of Chaotic Time Series

Abstract

Chaotic systems are sensitive to initial conditions. The exponential divergence of nearby trajectories limits the accuracy of the long-term prediction of a chaotic time series. Because of the deterministic governing equations of the underlying system, accurate short-term prediction of a chaotic time series is possible. Various approaches have been used to forecast a chaotic time series, the most popular of which is the first-order approximation of the local dynamics in the embedded state space. Simultaneously, various strategies for modeling a time series by a complex network have also been developed. Nonetheless, time-series induced networks have received little attention in terms of forecasting time series. This paper proposes a method based on symbolic dynamics for constructing a weighted network from a given time series and provides a strategy for forecasting a time series using the weighted network. We demonstrate the approach’s effectiveness by predicting a chaotic time series. The results are then compared to those obtained using the linear first-order approximation method. The proposed method is straightforward, computationally efficient, and parameter-free.