Dynamical Variety of Shapes in Financial Multifractality

Figure 2

(a) For the S&P500 from January 03, 1950, to December 29, 2016, the sequence of singularity spectra calculated within a rolling 20-year window. The calendar date assigned to each corresponds to the end point within a window. This window is moved with the step of 20 points which corresponds approximately to one calendar month. The black sold line corresponds to the left and the blue line to the right side of . (b) Projections of of (a) onto the time plane. The red line illustrates displacement of the maxima of in the consecutive windows. Vertical dashed lines indicate the Black Monday of October 19, 1987; burst of the Dot-com bubble in March 10, 2000; and bankruptcy of Lehman Brothers in September 15, 2008.

(a)

(b)