On the basis of detrended fluctuation analysis (DFA), a new method, moving cut data-DFA (MC-DFA), was presented to detect abrupt dynamic change in correlated time series. The numerical tests show the capability of the presented method to detect abrupt change time-instants in model time series generated by Logistic map. Moving DFA (MDFA) and approximate entropy (ApEn) can provide some information such as a single time-instant of abrupt dynamic change, but both of them cannot exactly detect all of the abrupt change regions. Some traditional methods, such as moving t-test, Cramer method, Mann-Kendall test and Yamamoto method, even cannot provide any information of abrupt dynamic change in these model time series. Meanwhile, results showed that windows sizes and strong noise have some less effect on the MC-DFA results. In summary, MC-DFA provides a reliable measure to detect the abrupt dynamic change in correlated time series, and perfectively make up the deficiencies of MDFA and ApEn. The applications in daily surface air pressure records further verify the validity of the present method.

Abstract. Based on Detrended Fluctuation Analysis (DFA), we propose a new method -Moving Detrended Fluctuation Analysis (MDFA) -to detect abrupt change in dynamic structures. Application of this technique shows that this method may be of use in detecting time-instants of abrupt change in dynamic structures and we even find that the MDFA results almost do not depend on length of subseries, and are less affected by noise.

An abrupt change occasionally occurs when the dynamical system suddenly shifts from one stable state to a new state, which can take place in many complex systems, such as climate, ecosystem, social system, and so on. In order to detect abrupt change, this article presents a novel method -sliding transformation parameter (STP) on the basis of skewness change and the Box-Cox transformation. Tests on model time series and 1000 simulated daily precipitation data show the ability of the present method to identify and detect abrupt change of probability density function. The applications of STP in daily precipitation data show that there is an abrupt climate change between 1979 and 1980 in the selected observational stations, which is almost the same with the result obtained by approximate entropy (ApEn). Furthermore, it is found that the sample sizes of sliding windows have some influence on the Lambda parameter of the Box-Cox transformation, but it does not significantly affect the varying trend of the parameter and the identification of the change point in annual or interannual time scale. Comparing STP with the coefficient of skewness and kurtosis, ApEn, and some statistics approaches (e.g. percentiles and annual maxima), we find that the performance of the present method is much better than that of these methods.

An abrupt climate change means that the climate system shifts from a steady state to another steady state. Study on the phenomenon and theory of the abrupt climate change is a new research field of modern climatology, and it is of great significance for the prediction of future climate change. The climate regime shift is one of the most common forms of abrupt climate change, which mainly refers to the statistical significant changes on the variable of climate system at one time scale. These detection methods can be roughly divided into five categories based on different types of abrupt changes, namely, abrupt mean value change, abrupt variance change, abrupt frequency change, abrupt probability density change, and the multivariable analysis. The main research progress of abrupt climate change detection methods is reviewed. What is more, some actual applications of those methods in observational data are provided. With the development of nonlinear science, many new methods have been presented for detecting an abrupt dynamic change in recent years, which is useful supplement for the abrupt change detection methods.

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