Nonlinear Time Series Analysis

The subject of this thesis is nonlinear time series analysis, which concerns with the identification, predicting, and controlling of nonlinear systems.On the theoretical fundamental of our works, we demonstrate the prevalence of chaos in sampling series of dynamical flows and a novel corollary of fractal delay embedding prevalence theorem: fractal delay embedding self-determined theorem, which is the math meaning of nonlinear autoregressive model. We discuss the theory of linear prediction identification, demonstrate the insufficiency of linear model family. Moreover, we introduce the theory of discrete probability entropy, propose a novel statistical index: Nonlinear Irreducible Autocorrelation (NIA), which is a development of the theory of discrete probability entropy and is of very important significance to nonlinear prediction model identification.On the identification of nonlinearity and chaos, We propose the robust criterion of the determination and nonlinearity test, a novel fuzzy clustering algorithm to identify the geometrical structure of underlaying attractors in phase space, and a novel definition to measure the dimension of underlaying attractors by a robust way. The advantages of the above proposals are demonstrated by means of simulations.On nonlinear denoise, prediction model identification and chaotic time series prediction, we propose the criterion of optimal truncation of wavelet-based nonlinear denoise, develop a novel NIA-based method to validate the optimal autoregressive order of nonlinear autoregression models, and demonstrate the advantage of these proposals by means of simulations.On modeling and control of complex systems, we implement stock prediction by means of TLRN neural networks, describe OGY chaos controlling method, demonstrate the inherent nonlinearity of speech time series and the necessity of nonlinear speech features extraction and classification, suggest a set of available index to achieve nonlinear speech feature extraction, which advantages demonstrated by means of simulations..