Nonlinearity, Chaos Theory and the DJIA by Victor E. Krynicki, Ph.D.
Here's a fresh look on using nonlinear systems and chaos theory to understand the markets.
Concepts deriving from nonlinear systems and chaos theory have begun to be applied to understand
stock market behavior. In a STOCKS & COMMODITIES article, Hans Hannula presented an attempt to apply
the concept of the strange attractor to major price swings, pointing out that stock market behavior evinces
both linear and nonlinear domains.
Within a linear domain of the stock market, a proportional relationship controls price moves, since input
force is proportional to output force in a linear system. But movement out of linear domains — where
input and output no longer relate in a direct, predictable manner—frequently occurs, with
non-proportional relationships then being evident. An extreme example occurred in the months and
weeks leading up to October 13, 1989 (Figure 1). The Dow Jones Industrial Average (DJIA) moved
upward in a linear channel, gradually carving successively higher highs and higher lows; it then moved
into a horizontal range shortly before October 13. On October 13, this uptrend's boundaries were not only
broken, but prices also did not fall in a linear manner. Rather, DJIA prices behaved like a rubber band that
had suddenly snapped, leading to abrupt and extreme changes in other market averages.