Fig. 3 shows the new predictions of the future of the US S&P 500 index using all the data from Aug. 9, 2000 to Dec. 16, 2003, illustrated by (continuous and dashed) black lines. Again, the continuous line is the fit and its extrapolation using the super-exponential power-law log-periodic function derived from the first order Landau expansion of the logarithm of the price, while the dashed line is the fit and its extrapolation by including in the function a second log-periodic harmonic. We also present the two previous fits (red lines) performed on Aug. 24, 2002 (shown in Fig. 2) for comparison, so as to provide an estimation of the sensitivity of the prediction and of its robustness as the price evolves. The blue dots show the daily price evolution from Aug. 9, 2000 to Dec. 16, 2003. The large (respectively small) ticks in the abscissa correspond to January 1st (respectively to the first day of each quarter) of each year.
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