Way Ahead of Mandelbrot in Several Aspects
Moreover, that there is any "theoretical
reformulation" of the idea of market self-affinity, as Mandelbrot
claims, is not evident from a close reading of his article. Allowing for
differences in terminology, there is nothing in the article that writers
about the Wave Principle have not already said except perhaps for the
material in his inset, which helps demonstrate that Elliott was right.
If there is any difference between Elliott’s and Mandelbrot’s
formulation of the thesis, it is the relative richness of the former.
For instance, the forms in Mandelbrot’s illustrations
are arbitrary,
making his specific depiction truly a rootless abstraction. He just
draws lines off the same sentence top of his head to simulate market
fractality. Elliott, in contrast, spent the better part of a decade
studying actual market price movements before coming to a conclusion
regarding the essential pattern that repeats at higher scales.
Mandelbrot depicts the market as three movements in each direction,
which entreats one to ask, "In the real world, why should the rising
lines be longer than the falling ones?" Elliott noticed that in the real
world, rising trends typically subdivide into five "waves" (Mandelbrot
calls them "pieces") and falling trends into three. This also happens to
be the minimal form, certain other things being equal, that allows both
fluctuation and progress in this type of system. Mandelbrot proposes no
specific pattern while nevertheless being forced to invent one for his
depiction. Elliott catalogued the forms that appear in the real world
and depicted them accordingly. One may attempt to dispute Elliott’s work
in this regard, but he may not dismiss it or ignore it.
Mandelbrot states:
On a practical level, this finding suggests that a
fractal generator can be developed based on historical market
data. The actual model does not simply inspect what the market did
yesterday or last week…. The charts created from the generators
produced by this model can simulate alternative scenarios based on
previous market activity.14
This is not a new idea that can now arise from
Mandelbrot’s "new" discovery. Developing a fractal generator based on
historical market data is exactly what Elliott did. Numerous
practitioners have gone back to the start of stock trading records to
produce "alternative scenarios based on previous market activity" as an
ongoing exercise. In 1986, my firm employed the Lockheed Corporation to
begin developing a computerized expert system that applies Elliott’s
model of market self-affinity to the task of stock market forecasting.
It considers stock market data going back to the start of the century
and ranks what our 1978 book15 terms "alternate counts" by
the degree to which they fit the ideal model.
