Zeev's Turnips Patch-No Politics (ZEEV)

[Train Guy]

Here's something interesting. It's got lots of math in it. Ok, I give, apparently it won't let me post the graphs no matter what I try so just click on the link at the top to see them. AAAAARRRRGGH. It wouldn't show them in preview, but now does.

http://www.ess.ucla.edu/faculty/sornette/prediction/index.asp#prediction

Prediction: The future of the USA stock market - Prediction date Nov 21, 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? In press in Quantitative Finance (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?. http://www.ess.ucla.edu/faculty/sornette/books.asp#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 prediction of the future of the US S&P 500 index performed on August 24, 2002. The continuous line is the fit and its extrapolation using the 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 August 9, 2000 to August 24, 2002 that are marked as black dots. The blue dots show the daily price evolution from August 25, 2002 to October 31, 2002. The ticks in the abscissa correspond to January 1st of each year.



Fig. 2 shows the new prediction of the future of the US S&P 500 index using all the data from August 9, 2000 to November 21, 2002 illustrated by black (continuous and dashed) 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 August 24, 2002 (shown in Fig. 1) 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 August 9, 2000 to November 21, 2002.