Stock Market Nonlinear Analysis and Prediction Toolkit

The Stock Market Nonlinear Analysis and Prediction Toolkit provides robust mathematical tools for financial time series research, particularly suited for uncovering market volatility patterns. This toolkit integrates multiple core algorithms that enhance analytical efficiency from various dimensions through optimized computational implementations.

In the complexity analysis module, the toolkit implements two classical methods: Higuchi Fractal Dimension method and Box-Counting Dimension method, which quantitatively measure the chaotic degree of market fluctuations. The code implementation includes efficient window-based calculations for handling large-scale financial datasets. For phase space reconstruction, the toolkit employs Cao's method and GP algorithm to determine optimal embedding dimensions, combined with mutual information method for calculating time delay parameters, establishing a proper dynamical system model for subsequent predictions through matrix operations and nearest-neighbor search techniques.

The stability assessment module integrates Wolf's method and small data sets method to compute the largest Lyapunov exponents. The implementation uses numerical differentiation and iterative calculations to determine exponent signs, effectively identifying chaotic characteristics in markets. The prediction module contains single-step prediction based on Lyapunov exponents and a unique multi-step multiple prediction architecture, utilizing interpolation algorithms and error correction mechanisms to handle nonlinear features in financial data effectively.

The entire toolkit has been validated with real market data, maintaining algorithmic rigor while optimizing computational performance. It particularly excels at processing complex time series like high-frequency trading data through parallel computing optimizations. Users can flexibly combine different modules to construct complete analytical workflows from feature extraction to trend prediction, with each function providing clear input/output interfaces and parameter customization options.