Starting from the characterization of the past time evolution of market prices in terms of two fundamental indicators, price
velocity and price acceleration, we construct a general classification of the possible patterns characterizing the deviation
or defects from the random walk market state and its time-translational invariant properties. The classification relies on
two dimensionless parameters, the Froude number characterizing the relative strength of the acceleration with respect to the
velocity and the time horizon forecast dimensionalized to the training period. Trend-following and contrarian patterns are
found to coexist and depend on the dimensionless time horizon. The classification is based on the symmetry requirements of
invariance with respect to change of price units and of functional scale-invariance in the space of scenarii. This “renormalized
scenario” approach is fundamentally probabilistic in nature and exemplifies the view that multiple competing scenarii have
to be taken into account for the same past history. Empirical tests are performed on about nine to thirty years of daily returns
of twelve data sets comprising some major indices (Dow Jones, SP500, Nasdaq, DAX, FTSE, Nikkei), some major bonds (JGB, TYX)
and some major currencies against the US dollar (GBP, CHF, DEM, JPY). Our “renormalized scenario” exhibits statistically significant
predictive power in essentially all market phases. In contrast, a trend following strategy and + following strategy perform
well only on different and specific market phases. The value of the “renormalized scenario” approach lies in the fact that
it always selects the best of the two, based on a calculation of the stability of their predicted market trajectories.
PACS. 02.50.-r Probability theory, stochastic processes, and statistics – 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion – 89.90.+n Other areas of general interest to physicists