Fig. 1 shows 9 years of the evolution of the Japanese Nikkei index and almost 8 years of the USA S&P500 index, compared to each other after a translation described in the update of September 17, 2000 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. Note that extrapolating is often a risky endeavor and needs to be justified. In our case, the extrapolations, which give the forecasts, are based on the belief that these equations offered below embody the major forces in the market at the macroscopic scale. This leads to the possibility of describing several probable scenarios. We do not believe in the existence of deterministic trajectories but we aim at targeting the most probable future paths.