Paper: arXiv 2511.10365

Authors: Yilong Zeng, Boyan Tang, Xuanhao Ren, Sherry Zhefang Zhou, Jianghua Wu, Raymond Lee

Abstract

This paper introduces the Fractal-Chaotic Oscillation Co-driven (FCOC) framework, a novel paradigm for financial volatility forecasting that systematically resolves the dual challenges of feature fidelity and model responsiveness. FCOC synergizes two core innovations: our novel Fractal Feature Corrector (FFC), engineered to extract high-fidelity fractal signals, and a bio-inspired Chaotic Oscillation Component (COC) that replaces static activations with a dynamic processing system. Empirically validated on the S&P 500 and DJI, the FCOC framework demonstrates profound and generalizable impact. The framework fundamentally transforms the performance of previously underperforming architectures, such as the Transformer, while achieving substantial improvements in key risk-sensitive metrics for state-of-the-art models like Mamba. These results establish a powerful co-driven approach, where models are guided by superior theoretical features and powered by dynamic internal processors, setting a new benchmark for risk-aware forecasting.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a solid theoretical foundation combining Multifractal Analysis (OSW-MF-ADCCA) and chaotic dynamics (Lee Oscillator) for volatility forecasting. Empirical testing on major financial indices (S&P 500, DJI) demonstrates substantial performance gains across modern deep learning architectures like Transformers and Mamba.

Research Flowchart

  flowchart TD
    A[Research Goal: Improve Volatility Forecasting via FCOC Framework] --> B[Data Inputs: S&P 500 & DJI Equity Indices]
    B --> C[Methodology: Combine Fractal Features & Chaotic Processing]
    C --> D[Fractal Feature Corrector: Extract High-Fidelity Signals]
    C --> E[Chaotic Oscillation Component: Replace Static Activations]
    D --> F[Computational Phase: Train & Evaluate Neural Networks]
    E --> F
    F --> G[Key Outcomes: Enhanced Transformer Performance & Superior Risk-Aware Forecasting in Mamba]

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0 of 48 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.