Applying the Modified CC Method to Calculate Time Delay and Embedding Dimension

The modified CC (Correlation Integral) method can be effectively applied to calculate time delay and embedding dimension for time series analysis. This enhanced algorithm not only performs accurate data processing but also provides additional control parameters that allow for finer regulation of the computational procedure. Key implementation aspects include: the calculation of correlation integrals using optimized distance metrics, automated determination of optimal time delay through mutual information analysis, and systematic selection of embedding dimension using false nearest neighbor detection. The method demonstrates high computational efficiency, enabling rapid processing of large-scale datasets through vectorized operations and parallel computing techniques. Practical code implementation typically involves functions for phase space reconstruction, correlation dimension estimation, and convergence testing to ensure reliable results. Overall, the modified CC method represents an advanced data processing technique suitable for diverse applications in nonlinear time series analysis, chaos theory, and complex system modeling.