The research of dynamic structure abrupt change of nonlinear time series

Abstract

For a long time in the past, researches of time series were often based on their external characters and used linear and statistical methods. However, most actual systems are nonlinear, nonstationary and complicated, which increased the diffculties in treating them. The research of abrupt change is one of most important research aspects of nonlinear time series, for which the traditional method based on the external characters of data and using linear process lacks enough physical foundation, and has obvious limitations. How to find out the essence of complicated systems from time series, in other words, to check the abrupt change in dynamical structure of actual data series is a really important problem pending solution. In the present paper, we present a new method——the dynamical correlation exponent segmentation algorithm for checking dynamical abrupt change based on the dynamical lag correlation exponent. The validity of this method is verified by constructing an ideal time series and put it to test. It was found that a few noise spikes have little influence, but continuously distributed white noise has some influence to this new method. Comparison with conventional t-test and Yamamoto method was made to show the relative merits of the methods.