A Noise Resilient Approach for Robust Hurst Exponent Estimation

2025-10-06

AI Summary

Additive noise in real-world measurements severely degrades the accuracy of wavelet-based Hurst exponent (H) estimation, hindering reliable quantification of self-similarity. Method: We propose a noise-robust multiscale H estimation framework that constructs inter-scale correlation features from wavelet energy pairs, integrates them within the Average Layer-wise Hurst Estimation (ALPHEE) paradigm, and employs a lightweight neural network for adaptive fusion—without requiring predefined scale-level constraints. A noise-aware control mechanism is introduced to dynamically regulate feature aggregation. Contribution/Results: The method preserves estimation accuracy on noise-free data comparable to ALPHEE while substantially enhancing robustness to additive noise, overcoming inherent limitations of conventional averaging strategies. Experiments across diverse noise intensities demonstrate a 30–52% reduction in H estimation error. This establishes a new paradigm for reliable characterization of nonstationary, long-range dependent signals.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Ensemble Methods
• Search and Optimization: Heuristic Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Enhancing Hurst exponent estimation accuracy under noise
• Improving wavelet-based methods' robustness to additive noise
• Developing adaptive neural network approach for noisy signals

Innovation

• Enhanced ALPHEE method with noise mitigation
• Neural network replaces traditional averaging for estimates
• Adaptive learning maintains accuracy in noisy conditions