One-Dimensional Time Series Correlation Dimension Computation

This MATLAB-based program computes the correlation dimension for one-dimensional time series data, facilitating better data analysis and understanding. The core functionality involves transforming a 1D time series into appropriate vector representations and calculating its correlation dimension using efficient numerical methods. Key features and implementation advantages include: - User-friendly interface: Simply input your time series data, and the program automatically computes the correlation dimension using built-in algorithms for phase space reconstruction and distance calculations. - Computational efficiency: The program employs optimized algorithms including delayed coordinate embedding for phase space reconstruction and efficient pairwise distance computations using vectorized MATLAB operations, ensuring fast processing even for large datasets. - Modular architecture: Designed with modular components for phase space reconstruction, correlation sum calculation, and dimension estimation, allowing easy customization and extension of specific algorithmic components. The code structure separates core functions like embedding dimension selection, time delay calculation, and scaling region identification for maintainability. Algorithm implementation details: The program utilizes the Grassberger-Procaccia algorithm for correlation dimension estimation, implementing functions for: 1. Time delay embedding using the mutual information method 2. Correlation integral calculation with optimized distance computations 3. Scaling region identification through linear regression in log-log plots This program aims to assist researchers and analysts in characterizing the complexity of time series data through robust dimension estimation techniques.