Characterization of detrended fluctuation analysis in the context of glycemic time series

There is a growing interest in the analysis of hyperglycemia and its relationship with other pathologies. The level of glucose in blood is regulated by the flux/reflux and controlled by hyperglycemia hormones and hypoglycemic insulin. Glycemic profiles are characterized by a nonlinear and nonstationary behavior but also influenced by circadian rhythms and patient daily routine which introduce quasi-periodic trends into them. This type of signals are commonly analyzed by Detrended Fluctuation Analysis (DFA) which states that the control system in charge of regulating the glucose level usually holds a long-range negative correlation. But there is an inconsistency about the windowing lengths, as no standard or rules are set. This work studies the influence of the windowing length sequence, and shows that there is a need for selecting the optimal values in order to obtain a good differentiation between different groups, and these values are somehow determined by signal characteristics.