Fig. 6 extends Fig. 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 Fig. 3, we have generated 10 realizations of an artificial S&P 500 by adding A GARCH noise to the black solid line. The innovations of the used GARCH noise have been drawn from a Student distribution with 3 degrees of freedom with a variance equal to that of the residuals of the fit of the real data by the black continuous curve. We have then fitted each of these 10 synthetic noisy clones of the S&P 500 (shown as the blue dots) 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&P 500 price trajectory is shown as the red wiggly line.

 

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