Fig. 7
From: Quasi-differentiation and its applications to noisy time series data from complex systems
(a) The daily closing prices (blue) and daily returns (red) of the DJIA, between 2 Jan 2003 and 29 Dec 2023 (a total of 5,285 trading days). (b) The quasi-derivatives of the mean (green) and variance (blue) for the daily returns of the DJIA between 2 Jan 2003 and 29 Dec 2023 (5285 trading days, obtained using a pair of sliding time windows with width \(w=100\) trading days. Also shown in red is the daily closing price of the DJIA, while the zero value of the quasi-derivatives of the mean and the variance is shown as the blue dashed line. In this figure, the variance quasi-derivative was multiplied by 5, so that it is visually comparable to the mean quasi-derivative. Based on these two quasi-derivatives, we are most confident of the two sudden events marked as yellow shaded regions.
