Volume 141, Number 6, March 2023
|Number of page(s)
|Statistical physics and networks
|17 March 2023
Equivalence between time series predictability and Bayes error rate
1 School of computer science, Northwestern Polytechnical University - Xi'an 710129, China
2 Big Data Research Center, University of Electronic Science and Technology of China - Chengdu 611731, China
Received: 29 November 2022
Accepted: 6 March 2023
Predictability is an emerging metric that quantifies the highest possible prediction accuracy for a given time series, being widely utilized in assessing known prediction algorithms and characterizing intrinsic regularities in human behaviors. Lately, increasing criticisms aim at the inaccuracy of the estimated predictability, caused by the original entropy-based method. In this paper, we strictly prove that the time series predictability is equivalent to a seemingly unrelated metric called Bayes error rate that explores the lowest error rate unavoidable in classification. This proof bridges two independently developed fields, and thus each can immediately benefit from the other. For example, based on three theoretical models with known and controllable upper bounds of prediction accuracy, we show that the estimation based on Bayes error rate can largely solve the inaccuracy problem of predictability.
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