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Error Statistics of Time-Delay Embedding Prediction on Chaotic Time Series

机译:混沌时间序列的时延嵌入预测误差统计

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This project investigates a statistical method for analyzing the error on predictions made through the process of time-delay-embedding of chaotic time series. A very remarkable result from the study of chaotic dynamical systems shows that present in almost any single time series is information from all the variables of the state space. The technique of time-delay-embedding provides a method for making predictions on the evolution of this time series. In this method of prediction, one must choose a parameter k, the number of near neighbors in phase space to fit the model to. This project answers the question by describing an algorithm for determining the largest k such that the model adequately fits the data. A prediction is then made from this model along with confidence intervals which measure the reliability of the expected response. While this project involved many different data sets, the purpose was to develop a general algorithm which could theoretically be used on any chaotic system.

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