Dynamical Variety of Shapes in Financial Multifractality

Figure 9

Projections onto the time plane of the sequence of singularity spectra calculated within a rolling 20-year window for both the average spectrum (a) and (b) the artificial index of the 9 companies of Figure 8. The calendar date assigned to each corresponds to the ending point within a window. This window is moved with the step of 20 points which corresponds to approximately one calendar month. The red line illustrates displacement of the maxima of in the consecutive windows. Vertical dashed lines indicate the Black Monday of October 19, 1987, and bankruptcy of the Lehman Brothers in September 15, 2008, while the dotted ones indicate October 1990 and April 1994. The bottom three panels display the corresponding Hurst exponents (c1), widths (c2), and the asymmetry coefficients (c3).