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

The complexity of stock price fluctuations stems from its multi-scale characteristics, nonlinear dynamic characteristics, and fractal structure. To better capture the fractal characteristics of stock prices, this paper creatively proposes a prediction method based on fractal feature extraction and deep learning. First, the generalized Hurst exponent Hq, high-order fractal dimension FDq, and multifractal spectrum MFSq are combined to characterize the long-range correlation and local complexity of stock price series from different scales. In addition, Rényi entropy and generalized fractional Brownian motion (GFBM) are introduced to enhance the descriptive ability of features. Secondly, a multi-scale fractal feature fusion mechanism (MSA) is designed to achieve feature aggregation in the time-frequency domain to improve the adaptability of the model to the nonlinear fluctuation pattern of stock prices. Finally, a multi-scale fractal loss function is constructed to integrate Rényi error, Hölder constraint and fractal spectrum deviation to enhance the ability of the model to maintain fractal structure. Experimental results show that the prediction performance of this method on multiple real market data is better than that of existing methods, and it shows better performance in terms of accuracy, stability and extreme volatility processing ability. This study provides a new theoretical framework for financial time series analysis and a new idea for the application of fractal theory in financial forecasting.