  A remarkable similarity in the behavior of the US S&P500 index from 1996 to
August 2002 and of the Japanese Nikkei index from 1985 to 1992 (11 years shift)
is presented, with particular emphasis on the structure of the bearish phases.
Extending a previous analysis of Johansen and Sornette [1999, 2000] on the
Nikkei index ``anti-bubble'' based on a theory of cooperative herding and
imitation working both in bullish as well as in bearish regimes, we demonstrate
the existence of a clear signature of herding in the decay of the S&P500 index
since August 2000 with high statistical significance, in the form of strong
log-periodic components. We offer a detailed analysis of what could be the
future evolution of the S&P500 index over the next two years, according to
three versions of the theory: we expect an overall continuation of the bearish
phase, punctuated by local rallies; we predict an overall increasing market
until the end of the year 2002 or at the beginning of 2003 (first quarter); we
predict a strong following descent (with maybe one or two severe up and downs
in the middle) which stops during the first semester of 2004. After this strong
minimum, the market is expected to recover. Beyond, our prediction horizon is
made fuzzy by the possible effect of additional nonlinear collective effects
and of a real departure from the anti-bubble regime. The similarities between
the two stock market indices may reflect deeper similarities between the
fundamentals of two economies which both went through over-valuation with
strong speculative phases preceding the transition to bearish phases
characterized by a surprising number of bad surprises (bad loans for Japan and
accounting frauds for the US) sapping investors' confidence.
