Using GP Algorithm to Determine Embedding Dimension and Fractal Dimension in Chaotic Time Series Prediction
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Resource Overview
Application of Gaussian Process (GP) algorithm for estimating embedding dimension and fractal dimension in chaotic time series prediction, with implementation insights for computational approaches.
Detailed Documentation
In chaotic time series prediction, we employ the Gaussian Process (GP) algorithm to determine both embedding dimension and fractal dimension. This algorithm measures system complexity by identifying recurring patterns within the time series data and utilizes these patterns to forecast future trends. The implementation typically involves constructing delayed coordinate vectors for phase space reconstruction and applying GP regression to model the underlying dynamics. Through this methodology, we achieve more accurate predictions of future behaviors and trends, moving beyond simple observational data analysis to capture the intrinsic nonlinear characteristics of chaotic systems.
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