Market Prediction Through Fractal Geometry
by Victor E. Krynicki, Ph.D.
Few have heard of fractal geometry and fewer still know how to use it. But it is a powerful tool with
which to analyze nonlinear systems and is the main alternative for analyzing systems that defy
development of predictive nonlinear equations. Krynicki presents a method by which to search for fractal
Since its inception, technical analysis has been dominated by linear and/or statistical smoothing,
averaging and estimation techniques. These techniques come in a vast a array of forms: linear regression,
quadratic regression, multiple correlation, oscillators, periodic regression, cycle estimation, moving
averages, weighted moving averages, percentage retracement targets, projected price lines and angles, to
name only a few. With specific reference to stock index analysis, these techniques have been applied to
the values of the stock index itself, to advances-declines, to up volume/down volume, to new highs/new
lows, and to a vast array of combinations or alternatives to these variables.
Market indices can be modeled as the output of a nonlinear dynamic system. Dynamics is the study of
motion in the broadest sense of the term; thus, "motion" refers to events such as the oscillations of a
pendulum, fluctuations in an animal population's density, appearance of chemical products in a reaction
vessel, fluid convection in a box system, fluctuations in outbreaks of disease, changes in economic data
such as monetary aggregates, and behavior of market indices.
On the other hand, "nonlinear" dynamic systems do not have a straightforward proportional relationship
between variables. In a nonlinear system, small changes in one variable can have a nonproportionally
large impact on other variables and the behavior of the system as a whole. Much recent work in nonlinear
systems has focused on chaos. "Chaos" can be defined in a variety of ways, but overall, the term refers to
a deterministic dynamic system that settles or dissipates into a bounded area. Within this area, the
system's behavior appears to be random even though deterministic equations are present.