Hurst Space Analysis, data clustering technique for long-range correlated time series

Abstract

It was shown for variables across different complex systems that their fluctuation functions calculated with detrending methods of scaling analysis are rarely, as in theory, ideal linear functions on log-log graphs of scale dependence. Instead, they frequently exhibit existence of transient crossovers in behavior, signs of trends that arise as effects of periodic or aperiodic cycles (Hu et al., 2001). The use of global and local wavelet transform spectral analysis (WTS) and their detrended fluctuation analysis (DFA) variants provides a possibility to detect these cyclic trends and to investigate their timing, nature and effects on the analyzed time series.