Schematic of initial steps in detrended fluctuation analysis (DFA). The first
panel (top left) schematizes the measured series. The second panel (top right)
schematizes the cumulative sum over time. The third panel (bottom left)
schematizes the fitting of linear trends to nonoverlapping bins of the
cumulative sum from the second panel, depicting the cumulative sum series in
grey curves, the trend lines in solid black lines, and the bin boundaries in
dashed black vertical lines. The fourth panel (bottom right) schematizes the
mean squared error (MSE) of residuals left over from each bin’s linear
fit in the bottom-left panel. In both bottom panels, the MSEs on the right
correspond to the linear fits on the left, for small, medium, and large
bins.