Status Updates From Why Stock Markets Crash: Cr...

​A HIERARCHY OF PREDICTION SCHEMES
The Simple Power Law
The “Linear” Log-Periodic Formula
The “Nonlinear” Log-Periodic Formula
The Shank’s Transformation on a Hierarchy ​of Characteristic Times

The causes of currency crises such as the 1997–98 Asian currency ​crises, can probably be
traced back to the interplay of countries’ structural imbalances and weak policies with shifts in market expec​tations, both amplifying each other to provide the principal source of ​​instability. In other words, the crisis resulted from the interaction ​of structural weaknesses and volatile international capital markets

Objects with ​fractional dimensions turn out to
possess the property of scale invari​ance. To capture this novel concept, we already mentioned that the word ​“fractal” was coined by Mandelbrot, from the Latin root fractus ​to capture the rough, broken, and irregular characteristics of the objects ​presenting at least approximately the property of scale invariance. This ​roughness can be present at all scales

Chaos has been widely popularized ​and has even been advocated by some as a useful description of stock ​markets. This, however, remains
too simplistic, as chaos theory relies ​on the assumption that only a few major variables interact nonlinearly ​​and create complicated trajectories. In reality, the stock market needs ​many variables to obtain a reasonably accurate description

the emergence of bubbles is explained as a self-organizing ​process of “infection” among
traders, leading to equilibrium prices that ​deviate from fundamental values. Assuming that the speculators’ readi​ness to follow the crowd may
depend on an economic variable, such as ​actual returns, above-average returns are reflected in a generally more ​optimistic attitude

Beyond the rationale to imitate discussed before, justification for imi​tative tendencies can
be found in evolutionary psychology. The ​point is that humans are rarely at their best when they use rational rea​soning. It can indeed be
demonstrated that “rational” decision-making ​methods are incapable of solving the natural adaptive problems our ancestors had to solve
reliably in order to survive and repro​duce.

The urn model can be generalized by changing the rules of addition ​of the new balls; that
is, how many new investors come into play, how do they do so, and how do they imitate the existing players so as to ​include more complex nonlinear behaviors