Author: Denis Avetisyan
Researchers have developed a novel deep learning framework that leverages the complex interplay of fractal patterns and chaotic dynamics to improve the accuracy of financial volatility predictions.
This paper introduces the Fractal-Chaotic Oscillation Co-driven (FCOC) framework, combining fractal feature extraction with a chaotic oscillation component for enhanced time series analysis.
Accurately forecasting financial volatility remains a persistent challenge due to the complex, often fractal and non-stationary nature of market dynamics. This paper introduces ‘FCOC: A Fractal-Chaotic Co-driven Framework for Financial Volatility Forecasting’, a novel deep learning architecture that synergistically combines enhanced fractal feature extraction with a bio-inspired chaotic oscillation component. Empirical validation on the S\&P 500 and DJI demonstrates that FCOC not only revitalizes the performance of existing models like the Transformer, but also achieves substantial gains in risk-sensitive metrics for state-of-the-art architectures such as Mamba. Could this co-driven approach, guided by superior theoretical features and powered by dynamic internal processing, represent a paradigm shift in risk-aware financial forecasting?
The Limits of Conventional Forecasting
Traditional volatility models often fail to accurately capture the complex, non-linear dynamics of financial time series, leading to prediction errors and hindering effective risk management. A primary limitation is the assumption of simple distributions, unable to represent the heavy tails and skewness common in financial returns. Existing methods frequently overlook long-range memory and the multifractal nature of financial data, underestimating extreme events and mispricing derivatives. Reliance on static models restricts adaptation to changing market conditions. Every structural constraint diminishes the system’s ability to evolve and maintain stability.
A Novel Framework: Fractal Correction and Chaotic Oscillation
The FCOC Framework introduces a novel approach to volatility forecasting, combining a Fractal Feature Corrector and a Chaotic Oscillation Component. This architecture explicitly models the complexities of financial time series data. The Fractal Feature Corrector extracts high-fidelity fractal features, capturing scaling properties more robustly than stationary methods. This component distills relevant information while mitigating noise. Complementing this, the Chaotic Oscillation Component replaces static activation functions with a bio-inspired dynamic system, allowing adaptation to changing signals and capturing nuanced patterns. The synergistic interaction of these components achieved an $R^2$ of 0.5066 when tested on the DJI index.
Decoding Financial Complexity: Fractal Feature Extraction
The Fractal Feature Corrector employs the OSW-MF-ADCCA algorithm to compute asymmetric Hurst exponents, capturing long-range memory within time series data. This approach quantifies temporal dependencies often overlooked by traditional methods, differentiating between persistent and anti-persistent behavior. Extending the MF-ADCCA framework, this methodology facilitates a robust analysis of multifractal properties, constructing fractal features like Bipolar Variation. These features serve as inputs for a Transformer model designed to capture intricate patterns. Application of this system achieved an $R^2$ of 0.3829, a 210% increase over a baseline score of 0.1234, demonstrating enhanced predictive accuracy.
Dynamic Activation: Bio-Inspired Neural Networks
The Chaotic Oscillation Component (COC) introduces dynamic activation functions to financial time series modeling, moving beyond the limitations of static functions. Leveraging the Lee Oscillator, the system creates activation functions that adapt to changing input patterns, mirroring dynamic behavior in biological systems. The core principle centers on inducing controlled non-linearity for improved capture of complex dependencies. Empirical results demonstrate significant performance improvement, with the FCOC-Mamba model achieving a 92.5% improvement in $R^2$ on the DJI index. A streamlined COC-only Transformer further validated the concept, attaining an $R^2$ of 0.4413 – a 250% increase over a baseline score of 0.1234. These gains suggest that modeling non-linear relationships with adaptable activation functions is crucial for accurate forecasting. The ability to dynamically adjust activation functions provides a powerful mechanism for capturing volatility; documentation captures structure, but behavior emerges through interaction.
The framework detailed within this study underscores a fundamental principle of systemic resilience. It posits that accurate forecasting, particularly in complex financial landscapes, requires acknowledging inherent chaotic tendencies alongside fractal patterns. This aligns with John Locke’s observation: “All mankind… being all equal and independent, no one ought to harm another in his life, health, liberty, or possessions.” Just as Locke championed individual liberties needing defined boundaries, the FCOC framework demonstrates that volatility forecasting improves when acknowledging the boundaries – and potential disruptions – within chaotic systems. By integrating fractal feature extraction with a chaotic oscillation component, the study aims to provide a more robust and reliable model, anticipating weaknesses before they manifest as significant deviations.
The Horizon Beckons
The FCOC framework, by explicitly attempting to integrate the geometries of fractals with the dynamics of chaos, offers a potentially valuable, if complex, perspective on financial time series. Yet, the very act of feature engineering, even within a deep learning architecture, reveals an inherent tension. Each handcrafted fractal dimension, each oscillation parameter, represents a structural commitment—a narrowing of possibility. Every new dependency is the hidden cost of freedom. The pursuit of accuracy, therefore, is not simply a matter of adding layers or refining algorithms, but of understanding where structural imposition limits the system’s ability to adapt to genuinely novel states.
Future work must address the question of generalization. While improvements in forecasting accuracy are valuable, a truly robust system should demonstrate resilience across diverse market conditions – conditions inevitably outside the scope of any training dataset. The exploration of intrinsic dimensionality reduction techniques, coupled with a more nuanced understanding of how fractal characteristics emerge from underlying market microstructure, could prove fruitful.
Ultimately, the challenge lies not in predicting the unpredictable, but in building systems that are gracefully adaptive to uncertainty. The FCOC framework, as a step toward embracing complexity rather than suppressing it, points toward a future where models mimic the very systems they attempt to understand – self-organizing, evolving, and accepting of inherent limitations.
Original article: https://arxiv.org/pdf/2511.10365.pdf
Contact the author: https://www.linkedin.com/in/avetisyan/
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2025-11-14 11:36