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Do Markets Exhibit Chaotic-Fractal Behavior ?



During the last decade the word "chaos" has come to be used to refer to complex, apparently random behavior that can be described by the iterative (repeated) application of simple, deterministic (not stochastic) equations. One is compelled to ask:

Is there a simple mathematical
formula driving market activity ?


To some degree the markets "appear" to be chaotic. However, one of the essential characteristics of a purely chaotic system is its extreme sensitivity to initial conditions. A tiny change in values at the beginning of the time series produces drastic changes in behavior later on. However, it is obvious the financial markets do not exhibit such extreme sensitivity to initial conditions. Someone willing to sell a large block of shares is not going to change his mind simply because you decided to put in an order for one share. From this it is fair to say the markets are not purely chaotic.

Although a chaotic system is a collection of orderly, simple behaviors, modeling the market has turned out to be more difficult than anticipated. The problem is that chaotic systems can be unusually flexible and rapidly switch among their many different behaviors. (Scientific American, August 1993, p78). So the big question now becomes:

How many simple formulas comprise all the
behaviors of a market, and what are they?

One way to isolate these individual behaviors might be to expect that when a market is perturbed in just the right way (eg. a large drop in price), it would exhibit one of its many regular behaviors for a short time. Collecting these rarified behaviors might lead to powerful models.

In the meantime, constructing leading indicators is difficult because the semi-chaotic nature of the market causes its "memory" of past events to rapidly dissipate over time. This suggests there may be a limited forecast horizon for any market time series. To follow this matter further, download our report "Optimal Forecast Horizon" in the Special Reports department.


There are behavioral patterns in some dynamic systems that seem to exist at various levels of resolution. For example, have you ever looked at a chart of S&P500 and could not readily decide if they were hourly, daily, weekly, or monthly bars? When behavior looks similar at various scales of resolution, it is said to be "fractal".


Many specific patterns in the markets can be considered fractal, such as the classic "Head and Shoulders" pattern. Also, Elliot Waves are fractal, with waves embedded within waves within waves, etc.

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