Computational Algorithm for Box-Counting Dimension of 1D Time Series

This is a computational program written in MATLAB for calculating the box-counting dimension of one-dimensional time series, designed to assist researchers in time series analysis. The implementation is based on the box-counting method, which quantifies the fractal dimension of time series data by dividing the data space into progressively smaller boxes and counting the number of boxes containing data points. This algorithm is particularly useful for analyzing the complexity and multifractal characteristics of time series, providing detailed insights that enhance our understanding and prediction of temporal patterns. The code structure includes key functions for data preprocessing, box-size scaling, and logarithmic regression analysis to compute the dimension. Users can customize parameters such as box-size ranges and scaling factors through configurable input variables. The program's modular design ensures flexibility, allowing easy integration of advanced analytical methods like multifractal analysis or adaptive box-size selection. Furthermore, the program offers excellent extensibility and flexibility, supporting user-defined configurations for specific research requirements. Researchers can build upon this foundation to implement more sophisticated analytical approaches, such as weighted box-counting or high-dimensional extensions. In summary, this program provides robust support for understanding and analyzing time series data, serving as a valuable tool for both academic research and practical applications in signal processing and dynamical systems analysis.