C-C Method for Calculating Time Delay and Embedding Dimension

The C-C method is a nonlinear time series analysis technique used for calculating optimal time delay and embedding dimension parameters, primarily applied in phase space reconstruction. This approach utilizes statistical analysis to determine appropriate time delay parameters while simultaneously providing the optimal embedding dimension.

The main programs C_CMethod.m and C_CMethod_independent.m execute the complete computational workflow. The subfunction correlation_integral.m calculates the correlation integral, which represents a core computational step in the C-C method. This function quantifies system dynamics by statistically analyzing distance distributions between time series points through distance matrix calculations and threshold comparisons.

The disjoint.m function partitions the original time series into multiple disjoint subsequences to enhance computational efficiency and prevent biases from data overlap. The heaviside.m function computes Heaviside step function values, playing a critical role in correlation integral calculations by determining whether data points fall within specified threshold ranges through conditional checks.

The key advantage of the C-C method lies in its ability to jointly estimate time delay and embedding dimension parameters, eliminating the cumbersome process of separately calculating these parameters in traditional methods. This technique is particularly suitable for chaotic time series analysis and finds widespread applications in financial data analysis, biological signal processing, and climate system modeling domains.