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 Didier Sornette, Professor of Geophysics

Based on a theory of cooperative herding and imitation working both in bullish as well as in bearish regimes that we have developed in a series of papers, 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).

Why Stock Markets Crash: For a general presentation of the underlying concepts, theory, empirical tests and concrete applications, with a discussion of previous predictions, see the recent book, Why Stock Markets Crash.

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Our analysis [1,2] has confirmed that the USA stock market antibubble has entered the second-order Landau regime. The first figure shows the modeling and prediction of the US S&P 500 index from 2000/08/21 to 2005/08/16 using the second-order Landau LPPL formula as well as the third-order Landau LPPL formula (LPPL stands for log-periodic power law). See [3,4] for a derivation and use of the third-order Landau formula in the context of the Nikkei antibubble from 1990 to 2002. The second figure shows the modeling and prediction of the Value Line Arithmetic Index.

We have included the third-order Landau LPPL forecast because we believe it is possible that the market is undergoing a transition from the second-order regime that started approximately at the end of 2002 to the third-order regime, after more than 2.5 years. We note the very large arch of the fit with the second-order Landau LPPL formula, which suggests (technically) a significantly stronger nonlinearity than previously experienced during the Nikkei antibubble from 1990 to 2002.

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Figures 3 and 4 show the same two indices (US S&P 500 and Value Line Arithmetic Index) together with 20 scenarios. These two figures are presented to remove the misleading impression given by the two preceding figures and some of our previous updates, that our forecasts are deterministic. Actually, they only represent a most probable outcome. To make this statement more precise, we generate 20 equiprobable scenarios by using a so-called bootstrap technique. The idea is simple. Our model assumes that the price trajectory results from the interplay between organizing ``forces'' and stochastic influences. Thus, the residues or differences between our fits and the prices give an estimate of the stochastic influences. By resampling these stochastic influences, we create artificially different pasts, which can then each be fitted by our two formulas, each past thus providing a plausible scenario for the future.

Technically, we have proceeded as follows. First, we fit the real time series (S&P 500 and VAY) using the second-order Landau LPPL formula. Thus, we obtain a residuals time series (one for each price). This residual time series is divided into sub-series with a time span of 21 trading days (almost a month). Then we reshuffle the residuals in the monthly scale to obtain new reshuffled time series. Then we fit the new time series using both the second-order and the third-order Landau LPPL formulae. The reshuffling and fit are performed 10 times, giving 10 additional future scenarios for each formula.

It is interesting to note that, while most of the scenarios are bearish on the S&P500, there is the potential (3 out of 20) for a continuation of a moderate growth over the next year. In contrast, for the Value Line Arithmetic Index, most of the scenarios forecast a flat or slightly increasing market over the next year.

[1] Zhou, W.-X. and D. Sornette, Testing the stability of the 2000 US stock market "antibubble", Physica A 348, 428-452 (2005) (e-print at http://arxiv.org/abs/cond-mat/0310092).

[2] Zhou, W.-X. and D. Sornette, Fundamental factors versus herding in the 2000-2005 US stock market and prediction, in press in Physica A (http://arxiv.org/abs/physics/0505079).

[3] Johansen and D. Sornette, Financial ``anti-bubbles'': log-periodicity in Gold and Nikkei collapses, Int. J. Mod. Phys. C 10(4), 563-575 (1999) (http://xxx.lanl.gov/abs/cond-mat/9901268)

[4] A. Johansen and D. Sornette, Evaluation of the quantitative prediction of a trend reversal on the Japanese stock market in 1999, Int. J. Mod. Phys. C Vol. 11 (2), 359-364 (2000) (http://arXiv.org/abs/cond-mat/0002059)

THIS IS AN EXPERIMENT PERFORMED IN REAL TIME AND WE WILL CONTINUE UPDATING EVERY MONTH.

REMEMBER THAT this analysis is for academic purposes only and must not be construed as investment or trading advice.