Phase Space Reconstruction of Time Series Using CC Algorithm for Delay Time and Embedding Dimension Selection

This article explores phase space reconstruction for time series analysis, focusing on the implementation of the CC (Cao's method) algorithm for selecting appropriate delay time and embedding dimension parameters. The proper selection of these parameters is crucial as it directly impacts the quality of reconstructed dynamics and subsequent analysis of underlying patterns in time series data. We provide a detailed explanation of the CC algorithm implementation, including how to compute correlation integrals and determine optimal parameters through statistical analysis. Practical code implementation considerations are discussed, such as calculating mutual information for delay time selection and using false nearest neighbors method for embedding dimension determination. The methodology's applications are demonstrated across various time series types, including how to handle implementation challenges like computational efficiency and parameter optimization. Through this article, readers will gain comprehensive understanding of time series analysis fundamentals and learn effective techniques for applying these principles to solve real-world data analysis problems.