A G British Kingdom
Chaos is evident just about everywhere: in lightning, weather patterns,
earthquakes, and financial markets. It may appear to be a random event,
but it isn’t. In a nutshell, chaos is a nonlinear, dynamic system that
appears to be random but is actually a higher form of order.
Social and natural systems, including private, governmental, and
financial institutions all fall within this category. People design
these complex systems only to find that these systems take on a life of
their own. Each of the system networks is sustained by complex feedback
loops that re-enter the system at unpredictable points in their cycles.
These feedback loops create an illusion of randomness.
When we discuss Chaos theory and trading, we are trying to define an
apparently random event in the marketplace that has some degree of
predictability. In order to do this we need a tool that is a
representation of order from chaos. The tool that we will use here is
the fractal. The fractal is commonly defined as
object with self-similar individual parts. In the markets, a fractal can
be thought of as an object or “time series” that appears similar across
a range of scales. Markets look this way when you compare a 3 minute
time scale to a 30 minute time scale to a 3 day time scale. Each frame
may zigzag a little differently, but when viewed from afar they have
similar attributes on each scale.
Almost all chaotic systems have a quantifying measurement known as a
fractal dimension. The fractal dimension is a non-integer dimension that
describes how an object takes up space. Objects in space (and the
systems that create them) are infinitely complex. If you examine any
object with a microscope, more detail is revealed as the scale changes.
In addition to levels of detail, most objects in nature demonstrate
self-similarity, the organizing principal of fractals. Because of this,
fractals will maintain their dimension regardless of the scale used.
This is evident in natural phenomena such as mountains, coastlines,
clouds, hurricanes and lightning.
Similarity across scales is important in trading because each time frame
of a market will have a similar fractal pattern. This also demonstrates
that markets are natural phenomena rather than mechanical processes. As
such, markets can only be forecasted reliably with principles applicable
to nonlinear, natural systems. Fractal geometry is such a tool