Minimizing the effect of trends on detrended fluctuation analysis of long-range correlated noise

Detrended fluctuation analysis (DFA) has been proposed as a robust technique to determine possible long-range correlations in power-law processes (Phys. Rev. E 49 (1994) 1685–1989). However, recent studies have reported the susceptibility of DFA to trends [(Phys. Rev. E 64 (2001) 011114–011133)] which give rise to spurious crossovers and prevent reliable estimation of the scaling exponents. Inspired by these reports, we propose a technique based on singular-value decomposition (SVD) of the trajectory matrix to minimize the effect of linear, power-law, periodic and also quasi-periodic trends superimposed on long-range correlated power-law noise. The effectiveness of the technique is demonstrated on publicly available data sets [(Phys. Rev. E 64 (2001) 011114–011133)].