A criterion for the determination of optimal scaling ranges in DFA and MF-DFA

Temporal scaling phenomena in groundwater-floodplain systems using robust detrended fluctuation analysis

“…To the best of our knowledge, the following three publications introduced methods for objective 243 fractal behaviour identification using DFA: (Echeverria, Rodriguez et al 2016, Gulich, Zunino 2014, 244 Grech, Mazur 2013. The most recent method (Echeverria, Rodriguez et al 2016) identifies a 245 transition range for the change in scaling behaviour rather than a point at which change occurs.…”

“…The most recent method (Echeverria, Rodriguez et al 2016) identifies a 245 transition range for the change in scaling behaviour rather than a point at which change occurs. The 246 second method uses the coefficient of determination (R 2 ) (Gulich, Zunino 2014) The novelty of the r-DFAn method is that it explicitly determines the statistical significance of 254 adjacent scaling regimes while taking into account the total number of scaling regimes with the help 255 of the multiple comparison procedure as previously explained. 256…”

Very prolonged practice in block of trials: Scaling of fitness, universality and persistence

“…It is known in the literature that the scaling range chosen for fitting the power law can disturb the numerical results [44]. We have used the range [6,192] in log scale for all the fits, and a brute-force algorithm [45] corroborates our approximations for h and the general profile of the fluctuations.…”

Study on nature of crossover phenomena with application to gearbox fault diagnosis

“…One possibility is to study the local exponents using the derivative scaling-law curve, as suggested by Govindan et al [24], Bashan et al [25] and Lopez et al [26]. However, the series usually have derivative discontinuities, making it very hard to apply in the case of multiple crossover points [27]. Another approach is to unveil the location of the crossover points by utilizing regression models with strict statistical sense.…”