Chaotic Time Series Prediction: Run for the Horizon

Gromov, Vasilii A.

doi:10.1007/978-3-030-71472-7_2

Cited by 1 publication

(4 citation statements)

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“…Te number of clusters increases with the size of their respective training set, whereas the number of nonpredictable points and the average error among the predictable ones decrease. A large-scale simulation for the Lorenz series [7] supports this conclusion.…”

Section: Introductionmentioning

confidence: 53%

“…Te importance of being able to make accurate predictions up to an increasing number of steps was named "Run for the Horizon" by the authors of the current paper in one of their previous publications [7]. Te series of works by Sangiorgio et al [10,30] (that culminated in a monograph [25] in 2021) approach multi-step-ahead forecasting by using neural networks, classic feed-forward, and recurrent architectures (LSTM) nets.…”

Section: Related Workmentioning

confidence: 99%

“…(6) Clustering 􏽢 S t+h and picking the center of a randomly chosen cluster based on the sum of weights of its elements relative to the sum of weights of all possible prediction values (roulette wheel). (7) [mf] Choosing the mode of 􏽢 S t+h . (8) [mfp] Choosing the mode of 􏽢 S t+h and adding a small amount of uniformly distributed noise to it:…”

Section: Unifed Predictedmentioning

confidence: 99%

“…Tis paper is already published in the preprint given in the below link: "https://www.researchgate.net/publication/ 347239842_Prediction_After_a_Horizon_of_Predictability_ Non-Predictable_Points_and_Partial_Multi-Step_Predictio n_for_Chaotic_Time_Series" [38].…”

Section: Data Availabilitymentioning

confidence: 99%

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Prediction after a Horizon of Predictability: Nonpredictable Points and Partial Multistep Prediction for Chaotic Time Series

Gromov,

Baranov

2023

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This paper introduces several novel strategies for multi-step-ahead prediction of chaotic time series. Introducing a concept of “generalized z-vectors” (vectors of nonsuccessive time series observations) makes it possible to generate sets of possible prediction values for each point we are trying to predict. Through examining these sets, unified predictions are calculated, which are in turn used as a basis for predicting subsequent points. The key difference between the strategy presented in this paper and its conventional counterparts is the concept of “nonpredictable” points (points which the algorithm categorized as “incalculable” and excluded from the calculations altogether). The results obtained for the benchmark and real-world time series indicate that while typically the number of nonpredictable points tends to grow exponentially with the number of steps ahead to be predicted, the average error for predicted points remains small and nearly constant. Thus, we redefine the problem of multi-step-ahead prediction as a two-objective optimization problem: on one hand, we aim to minimize the number of nonpredictable points and the average error among the predictable ones. The resulting strategy demonstrates accurate results for both benchmark and real-world time series, with the number of predicted steps exceeding that of any other published algorithm.

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Section: Introductionmentioning

confidence: 53%