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Applications Of Nonlinear Dynamical Methods In Time Series Analysis

Posted on:2006-10-25Degree:DoctorType:Dissertation
Country:ChinaCandidate:N WangFull Text:PDF
GTID:1100360155960447Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
Nowadays, the application of time series analysis has already become very important in many fields, including mathematics, physics, chemistry, biology, medicine, information science and economics. Linear methods are pretty good as a tool, which can find some satisfying results in studies of time series analysis. However, the real time series we gathered are mostly nonlinear due to the essence of nature. Linear method only presents approximate results. It must need nonlinear method to reflect essence of the time series veritably. From the late of last century, nonlinear method has been developing vigorously, including chaos, fractal etc. This offered us an opportunity to analyze time series by means of nonlinear tools. There are many branches in the field of time series analysis using nonlinear tools, and nonlinear dynamical methods is one of them that springs up in these years.This paper focuses on the application of nonlinear dynamical methods in the analysis of time series. We researched in the next five fields.It presents a method of normalization of complexity base on surrogate, and applies the prevalent Surrogate Method into time series analysis, which successfully solves the difficult problems of the sensitiveness of time series to epoch length, sampling frequency and provides comparability of nonlinear index between time series. This method effects excellently in the analysis of EEG signals.At the same time, method of principle component cluster analysis based on Lyapunov exponent spectrum in this paper combines methods of statistics and nonlinear dynamical methods together. It can effectively make assortment between nonlinear time series from same class, and get good results in HRV analysis. A method of TSS (teacher select student) algorithm is presented by improving the method of principle component cluster analysis based on Lyapunov exponent spectrum. It can analyze unknown samples using known ones, and is suitable for the comparison of time series from same class. It also shows more application value in analysis of ECG signals.
Keywords/Search Tags:Nonlinear dynamical methods, Time series analysis, Lyapunov exponent spectrum, principle component cluster analysis, TSS algorithm, Surrogate, Normalization, High dimensional mode complexity, EEG, ECG, Phase space reconstruction
PDF Full Text Request
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