|  MAR 1992

Market Prediction Through Fractal Geometry by Victor E. Krynicki, Ph.D.

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. LINEAR, NONLINEAR 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.

by Victor E. Krynicki, Ph.D.