Prediction Date: May 18, 2003
Other Predictions: April 18, 2003March 18, 2003February 19, 2003January 16, 2003December 19, 2002November 21, 2002October 31, 2002
Based on a theory of cooperative herding and imitation working both in bullish as well as in bearish regimes, we have detected the existence of a clear signature of herding in the decay of the US S&P500 index since August 2000 with high statistical significance, in the form of strong log-periodic components.
Please refer to the following paper for a detailed description: D. Sornette and W.-X. Zhou, The US 2000-2002 Market Descent: How Much Longer and Deeper? Quantitative Finance 2 (6), 468-481 (2002) (e-print at http://arXiv.org/abs/cond-mat/0209065).
For a general presentation of the underlying concepts, theory, empirical tests and concrete applications, with a discussion of previous predictions, see Why Stock Market Crash?.
This figure shows 8 years of the evolution of the Japanese Nikkei index and 7 years of the USA S&P500 index, compared to each other after a translation of 11 years has been performed. The years are written on the horizontal axis (and marked by a tick on the axis) where January 1 of that year occurs. This figure illustrates an analogy noted by several observers that our work has made quantitative. The oscillations with decreasing frequency which decorate an overall decrease of the stock markets are observed only in very special stock markets regimes, that we have terms log-periodic "anti-bubbles". By analyzing the mathematical structure of these oscillations, we quantify them into one (or several) mathematical formula(s) that can then be extrapolated to provide the prediction shown in the two following figures.
Fig. 1 shows the predictions of the future of the US S&P 500 index performed on Aug.24,2002. The continuous line is the fit and its extrapolation using our theory capturing investor herding and crowd behavior. The theory takes into account the competition between positive feedback (self-fulfilling sentiment), negative feedbacks (contrariant behavior and fundamental/value analysis) and inertia (everything takes time to adjust). Technically, we use what we call a "super-exponential power-law log-periodic function" derived from a first order Landau expansion of the logarithm of the price. The dashed line is the fit and its extrapolation by including in the function a second log-periodic harmonic. The two fits are performed using the index data from Aug.9,2000 to Aug.24 2002 that are marked as black dots. The blue dots show the daily price evolution from Aug.25,2002 to May.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.
as figuras estão aqui:
http://www.ess.ucla.edu/faculty/sornette/books.asp#crash
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