Methods for Selecting Optimal Delay Time Interval and Embedding Dimension in Chaotic Time Series Analysis

In this paper, the authors conduct a systematic review of methods for selecting optimal delay time interval and embedding dimension in phase space reconstruction of chaotic time series. They propose a novel reconstruction method called the "false nearest neighbors method" that simultaneously considers both parameters. This method involves analyzing neighborhood relationships in the reconstructed phase space to identify optimal embedding parameters. Additionally, the authors introduce a minimum prediction error approach for parameter selection. This technique involves performing multiple reconstructions with different parameter combinations and calculating corresponding prediction errors through iterative testing, ultimately selecting the parameter set that yields the smallest prediction error. The implementation typically requires creating multiple phase space reconstructions using varying delay times and embedding dimensions, followed by prediction accuracy evaluation using metrics like mean squared error. In summary, this paper provides a comprehensive methodology for phase space reconstruction of chaotic time series, offering researchers enhanced understanding and practical application of these techniques through systematic parameter optimization approaches.