A Noise Resilient Approach for Robust Hurst Exponent Estimation

• URL: http://arxiv.org/abs/2510.04811v1
• Date: Mon, 06 Oct 2025 13:54:23 GMT
• Title: A Noise Resilient Approach for Robust Hurst Exponent Estimation
• Authors: Malith Premarathna, Fabrizio Ruggeri, Dixon Vimalajeewa,
• Abstract summary: A key property is self-similarity, quantified by the Hurst (H)<n>Wavelet-based methods are effective for estimating H due to their multi-scale analysis capability, but additive noise in real-world measurements often degrades accuracy.<n>We propose Noise-Controlled ALPHEE, incorporating noise mitigation and generating multiple level-pairwise estimates from signal energy pairs.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Understanding signal behavior across scales is vital in areas such as natural phenomena analysis and financial modeling. A key property is self-similarity, quantified by the Hurst exponent (H), which reveals long-term dependencies. Wavelet-based methods are effective for estimating H due to their multi-scale analysis capability, but additive noise in real-world measurements often degrades accuracy. We propose Noise-Controlled ALPHEE (NC-ALPHEE), an enhancement of the Average Level-Pairwise Hurst Exponent Estimator (ALPHEE), incorporating noise mitigation and generating multiple level-pairwise estimates from signal energy pairs. A neural network (NN) combines these estimates, replacing traditional averaging. This adaptive learning maintains ALPHEE's behavior in noise-free cases while improving performance in noisy conditions. Extensive simulations show that in noise-free data, NC-ALPHEE matches ALPHEE's accuracy using both averaging and NN-based methods. Under noise, however, traditional averaging deteriorates and requires impractical level restrictions, while NC-ALPHEE consistently outperforms existing techniques without such constraints. NC-ALPHEE offers a robust, adaptive approach for H estimation, significantly enhancing the reliability of wavelet-based methods in noisy environments.

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