GP Algorithm for Calculating Optimal Embedding Dimension and Delay Time in Time Series Phase Space Reconstruction

The GP (Grassberger-Procaccia) algorithm enables the calculation of optimal embedding dimension and delay time for time series phase space reconstruction. This method facilitates a deeper understanding of time series characteristics and evolutionary trends, thereby enhancing data analysis capabilities. By reconstructing time series in phase space, we can effectively capture underlying information patterns within the data to support more accurate predictions and decision-making processes. From an implementation perspective, the algorithm typically involves: 1. Computing the correlation integral for different embedding dimensions 2. Determining the delay time using mutual information or autocorrelation methods 3. Identifying the optimal embedding dimension through false nearest neighbors analysis Key functions in implementation may include: - Mutual information calculation for delay time selection - Correlation dimension estimation using the Grassberger-Procaccia method - False nearest neighbors percentage computation for dimension validation The algorithm outputs critical parameters that ensure proper reconstruction of the system's dynamics from observed time series data.