提出抗噪方法提升波动率指数估计精度，尤其在噪声环境下表现更优。
A Noise Resilient Approach for Robust Hurst Exponent Estimation
- 基于小波分析改进多尺度能量对估计，引入神经网络融合多组结果
- 在无噪数据中保持原方法精度，在有噪条件下显著超越现有技术
- 无需限制分析层级，适合真实世界含噪信号的长期依赖建模
理解信号在不同尺度上的行为对自然现象分析和金融建模至关重要。自相似性由赫斯特指数（H）量化，反映长期依赖关系。小波方法因具备多尺度分析能力，常用于估计H，但现实测量中的加性噪声会降低准确性。本文提出噪声可控的ALPHEE（NC-ALPHEE），在平均层级对赫斯特指数估计器（ALPHEE）基础上，通过噪声抑制并生成多组层级-能量对估计值，再由神经网络（NN）融合这些结果，替代传统平均。该方法在无噪情况下保持原有性能，有噪时仍能稳定表现。大量仿真显示：在无噪数据中，NC-ALPHEE与原方法精度相当；在噪声存在下，传统平均方法性能下降且需人为限制层级，而NC-ALPHEE无需此类约束，始终优于现有方法。该方法显著提升了小波基赫斯特指数估计在噪声环境下的可靠性。
原文摘要 · Abstract (English)
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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