For over 30 years now, a schism in the financial world has divided technical analysts, who believe that the market follows regular cycles, from quantitative analysts, who believe there are no cycles. Recent research, utilizing techniques developed in the physical sciences to analyze non-linear systems, suggests that the truth lies somewhere in between. The S&P 500 has non-periodic cycles governed by a chaotic, or fractal, attractor.

This attractor arises because the relations between the variables that govern market movements are non-linear. Non-linear systems are characterized by trends and long-term correlations. If the market is non-linear, then the widespread use of standard statistical analysis is questionable. In particular, the Efficient Market Hypothesis and the Capital Asset Pricing Model (in its current form) are suspect as workable theories.