Application of moving cut data-wavelet transformation analysis in dynamic structure mutation testing

Abstract

The scaling exponent is an effective nonlinear dynamic index, which can be used to detect the dynamic structure mutations of the correlation time series by the moving cut a fixed window technology. The immediacy and accuracy of scaling exponent is very important for detecting the series change points, however, some of the existing scale index calculation methods (such as rescaled range analysis and rescaled variance analysis) take none of these into account. Wavelet transform analysis can quickly decompose the sequence on different scales, and then the scaling index can be calculated by analyzing the scaling relation of wavelet coefficients on different scales, which has the characteristics of fast calculation speed and good convergence and memory saving. By moving cut window technology, in the present paper we put forward a new method, i. e., the moving cut data-wavelet transformation for detecting a series of dynamic structure mutations. The principle is that the removal of the data has little effect on the estimation of the scaling exponents of the correlation time series with the same dynamical properties. In order to test the performance of the method, first of all, the dynamic structure mutation analyses of linear ideal time series and nonlinear ideal time series are carried out by selecting different moving cut fixed windows. The test results show that the method can quickly and accurately detect the dynamic structure change points and intervals both in linear time series and nonlinear time series, besides, its calculation speed is obviously better than the moving cut data-rescaled range analysis and the moving cut data-rescaled variance analysis. It has strong stability, and depends less on the moving cut window length, which will have some advantages in the large data processing. At the same time, in order to detect the influence of noise on the method, the linear and nonlinear ideal time series are added to the white Gaussian noise (SNR=20, 25, 30 dB), respectively, and the results show that the method has a strong anti-noise ability with different moving cut window lengths, can still quickly and accurately detect the mutation point or interval in different noise additions. Finally, the method is used to detect the dynamic structure mutation of measured daily maximum temperature data of Foping station in Wei basin, the experimental results indicate that the mutation interval is consistent with the abrupt change in 1970's on a global scale, which further verifies the validity of the method.