Stock price dynamics prediction based on multi-scale fractals and deep learning.

Area of Science:

• Quantitative Finance
• Computational Finance
• Financial Time Series Analysis

Background:

• Stock price fluctuations exhibit complex multi-scale, nonlinear, and fractal characteristics.
• Existing methods often struggle to fully capture these intricate dynamics for accurate prediction.

Purpose of the Study:

• To develop a novel stock price prediction method leveraging fractal feature extraction and deep learning.
• To enhance the characterization of stock price series by incorporating advanced fractal metrics and entropy measures.

Main Methods:

• Utilized generalized Hurst exponent (Hq), fractal dimension (FDq), and multifractal spectrum (MFSq) for scale-specific characterization.
• Integrated Rényi entropy and generalized fractional Brownian motion (GFBM) to enrich feature representation.
• Developed a multi-scale fractal feature fusion mechanism (MSA) for time-frequency domain aggregation.
• Constructed a multi-scale fractal loss function incorporating Rényi error, Hölder constraint, and fractal spectrum deviation.

Main Results:

• The proposed method demonstrated superior prediction performance compared to existing techniques on real market data.
• Achieved enhanced accuracy, stability, and improved ability to handle extreme market volatility.
• The multi-scale fractal approach effectively captures nonlinear dynamics and maintains the inherent fractal structure of stock prices.

Conclusions:

• This research offers a new theoretical framework for financial time series analysis.
• Presents a novel application of fractal theory for improved financial forecasting.
• The developed method provides a robust tool for understanding and predicting complex financial market behavior.