The Application Of Nonlinear Time Series

Nonlinear time series is a new branch of nonlinear science and has been used in the other fields of science more and more widely. In this paper, Fibonacci series which is generated by sigma substitution is studied by Multifractal detrended fluctuation Analysis(MF-DFA). By analyzing the corresponding decimal Fibonacci series, for the first time, we show that the multifractal detrended fluctuation analysis method can reliably determine the multifractal scaling behavior of the series. Then, we apply Multifractal detrended fluctuation analysis method to study traffic time series, Multifractal behavior in traffic time series usually connected with different long-range (time-) correlations of the small and large fluctuations or (and) a broad probability density function for the values of the time series. Multifractal detrended fluctuation analysis (MF-DFA) is used to study the traffic speed fluctuations. It is demonstrated that the speed time series, observed on the Beijing Yuquanying highway, has a crossover time scale s_x, where the signal has different correlation exponents in time scales s > s_x and s < s_x. The long-range correlation was validated to be dominant by the method of comparing the MF-DFA results for original series to those obtained via the MF-DFA for shuffled series. Then, based on the traditional linear interpolation method, the non-linear repair method is proposed for the first time, namely fractal interpolation method, and applied to the data missing, which enhances the repair effect to a certain extent. At last, according to the phase space reconstruction technology, the chaos prediction of short-term traffic flow time series is studied. Case study using real data proves the validity of the method. The chaos prediction method overcomes shortcomings of tranditonal linear statistical analysis, such as poor anti-jamming ability and low information forecast, and has very important significance in practice.