Fig. 11
From: Quasi-differentiation and its applications to noisy time series data from complex systems
The integrated quasi-derivative \(H_w(t)\) of the Hurst exponent of the daily returns of DJIA, using sliding windows with widths (a) \(w = 128\) and (b) \(w = 256\) days. In both figures, the blue curve is \(H_w(t)\)estimated using the R/S method54,55, while the green curve is \(H_w(t)\)estimated using the KS-GHE(1) method62. The time periods where the two methods agree qualitatively with each other are shown as gray shaded regions. We also mark the Oct 2008 Lehman Brothers crash and the Mar 2020 COVID-19 crash as yellow shaded regions.
