V.10:3 (102-107): Market Prediction Through Fractal Geometry by Victor E. Krynicki, Ph.D.

V.10:3 (102-107): Market Prediction Through Fractal Geometry by Victor E. Krynicki, Ph.D.
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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 patterns.

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.

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