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Multi-Step-Ahead Prediction of Chaotic Time Series: Self-Healing Algorithm for Restoring Values at Non-Predictable Points
This paper proposes a new algorithm for the multi-step-ahead prediction of chaotic time series within the framework of the clustering-based forecasting paradigm. The introduction of the concept of non-predictable points enabled to avoid the exponential growth of the prediction error as a function of the number of steps ahead, which made it possible to develop algorithms that predict many Lyapunov times (and many steps) ahead –the price for this turned out to be that some points remained non-predictable.This study proposes a self-healingalgorithm, which is an iterative algorithm that takes the forecasts produced by the underlying prediction algorithmas input. At each iteration, the self-healing algorithm finds new possible predicted values, updates the status of the points from predictable to unpredictable, or vice versa, and calculates new single predicted values for the predictable points. This study proposes several new algorithms for calculating a single prediction value and algorithms for determining unpredictable points. Authors overviewedrecent studies with larger goals and broader viewpoints on parameter estimations, relevance tracking, and predictive features. Results: Our research revealed that the new instruments in particular indicators increased RMSE(root mean squared error)from 0.11 to 0.06 and decreased MAPE(mean absolute percentage error)from 0.38 to 0.04.Research was conducted on the selection of parameters for the self-healing algorithm, its assessment, and the prediction quality compared to the existing prediction algorithm