Nonlinear Time Series And Spectral Analysis Of Complex System

Complexity science is a new rising cross-discipline which mainly discusses the complex system and complexity including many fields. Complex system typically has a large number of simple components, and there are nonlinear interactions between the components, such as economic system, traffic system and biological system. Due to certain characteristics of complex system, it’s hard to study by linear methods which promotes the development of nonlinear science. The investigation of fractal theory is very important for nonlinear science. One of the main feature of fractal is its scale-invariant. Nowadays, it has been clarified that the existence of auto-correlations in economic system, traffic system, biological system and cross-correlations between sys-tem components. It is of great importance to develop suitable techniques to capture the scaling exponents and cross-correlation exponents. In order to find the correct scaling behavior of time series, we propose diverse techniques for minimizing the effects of different superimposed trends. In this paper, auto-correlations of several stock markets and cross-correlations between different stock markets are investigated by fractal meth-ods. Furthermore, existence and determination of long-range correlations of stock time series make it possible for forecasting. A new forecasting technique based on K nearest neighbor and empirical mode decomposition method is introduced to predict stock time series. Brain activity of biological system is a dynamical system more complex than economic and traffic system. We pointed out the study of electroencephalogram(EEG) is a crucial and challenging research subject. The synchronization of different frequency bands of EEG signal is analyzed in this paper, and some radical ideas which different from traditional views are being pointed out.Chapter1introduces the research background, object of study and main research techniques, furthermore, the important works of this paper.In Chapter2, three modifications of fluctuation analysis are proposed. Firstly, B-spline method is combined with MF-DFA for minimizing the effect of exponential trends and periodical trends superimposed in series; secondly, Laplace transform is used in DFA, R/S analysis, DMA, CC and DCCA method for minimizing external periodi-cal trends, and resembled the correlation and cross-correlation behavior of original time series; lastly, A new detrending method based on orthogonal V-system is devoted for eliminating power-law trends, periodical trends, combined trends and piecewise func-tion trends.Chapter3is dedicated to detrended cross-correlation analysis(DCCA). Firstly, the superposition rules are studied both in theoretical and experimental aspect. Secondly, the correlations of stock markets and cross-correlations between different stock markets are analyzed by applying DCCA technique. Finally, cross-correlations of stock markets based on time delay are discussed using time delay DCCA.Chapter4focuses on a new non-parameter forecasting tool. The new predict-ing method base on modified K nearest neighbor and empirical mode decomposition method, called EMD-KNN method, is given in this chapter. This method does not re-quire certain models or parameters, and only sufficiently large quantities of data which represent the underlying system. For testing forecasting accuracy, the results of EMD-KNN, KNN and ARIMA method are compared.Chapter5analyzes the synchronization of frequency bands in EEG signal. The researching object of this chapter is the EEG signal which is recorded by setting elec-trodes on human’s scalp. The EEG signal can be decomposed into five frequency bands by applying fourier transform and spectral analysis:δ,θ,α,σ andβ. We mainly follow two different parts to investigate the frequency bands, first part is synchronization of fre-quency bands during different sleep stages, second part is synchronization of frequency bands in transitions of sleep stages.Chapter6devotes to the summary and some further works.