
Fig. 6 extends figure 3 by performing a sensitivity analysis on
the 'zero-phase' Weierstrass-type function, in order to assess
the reliability and range of uncertainty of the prediction. Using
the fit shown in black solid lines in figure 3, we have generated
10 realizations of an artificial S&P500 by adding white noise
to the black solid line. The white noise (shown as the blue dots)
is drawn from a student distribution with 3 degrees of freedom
and with a variance equal to that of the residuals of the fit of
the real data by the black continuous curve of figure 3. We have
then fitted each of these 10 synthetic noisy clones of the S&P500
by our 'zero-phase' Weierstrass-type function. This yields the
narrow bundle of 10 curves shown here in magenta. This bundle of
predictions is very coherent and suggests a good robustness of
the prediction. The typical width of the blue dots give a sense
of the variability that can be expected around this most probable
scenario. The real S&P500 price trajectory is shown as the
red wiggly line.
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