This article is from the Nonlinear Science FAQ, by James D. Meiss jdm@boulder.colorado.edu with numerous contributions by others.

(Thanks to Bruce Stewart for Contributions to this answer)

In order to address this question, we must first agree what we mean by chaos,

see [2.9].

In dynamical systems theory, chaos means irregular fluctuations in a

deterministic system (see [2.3] and [3.7]). This means the system behaves

irregularly because of its own internal logic, not because of random forces

acting from outside. Of course, if you define your dynamical system to be the

socio-economic behavior of the entire planet, nothing acts randomly from

outside (except perhaps the occasional meteor), so you have a dynamical

system. But its dimension (number of state variables--see [2.4]) is vast, and

there is no hope of exploiting the determinism. This is high-dimensional

chaos, which might just as well be truly random behavior. In this sense, the

stock market is chaotic, but who cares?

To be useful, economic chaos would have to involve some kind of collective

behavior which can be fully described by a small number of variables. In the

lingo, the system would have to be self-organizing, resulting in low-

dimensional chaos. If this turns out to be true, then you can exploit the low-

dimensional chaos to make short-term predictions. The problem is to identify

the state variables which characterize the collective modes. Furthermore,

having limited the number of state variables, many events now become external

to the system, that is, the system is operating in a changing environment,

which makes the problem of system identification very difficult.

If there were such collective modes of fluctuation, market players would

probably know about them; economic theory says that if many people recognized

these patterns, the actions they would take to exploit them would quickly

nullify the patterns. Market participants would probably not need to know

chaos theory for this to happen. Therefore if these patterns exist, they must

be hard to recognize because they do not emerge clearly from the sea of noise

caused by individual actions; or the patterns last only a very short time

following some upset to the markets; or both.

A number of people and groups have tried to find these patterns. So far the

published results are negative. There are also commercial ventures involving

prominent researchers in the field of chaos; we have no idea how well they are

succeeding, or indeed whether they are looking for low-dimensional chaos. In

fact it seems unlikely that markets remain stationary long enough to identify

a chaotic attractor (see [2.12]). If you know chaos theory and would like to

devote yourself to the rhythms of market trading, you might find a trading

firm which will give you a chance to try your ideas. But don't expect them to

give you a share of any profits you may make for them :-) !

In short, anyone who tells you about the secrets of chaos in the stock market

doesn't know anything useful, and anyone who knows will not tell. It's an

interesting question, but you're unlikely to find the answer.

On the other hand, one might ask a more general question: is market behavior

adequately described by linear models, or are there signs of nonlinearity in

financial market data? Here the prospect is more favorable. Time series

analysis (see [3.14]) has been applied these tests to financial data; the

results often indicate that nonlinear structure is present. See e.g. the book

by Brock, Hsieh, LeBaron, "Nonlinear Dynamics, Chaos, and Instability", MIT

Press, 1991; and an update by B. LeBaron, "Chaos and nonlinear forecastability

in economics and finance," Philosophical Transactions of the Royal Society,

Series A, vol 348, Sept 1994, pp 397-404. This approach does not provide a

formula for making money, but it is stimulating some rethinking of economic

modeling. A book by Richard M. Goodwin, "Chaotic Economic Dynamics," Oxford

UP, 1990, begins to explore the implications for business cycles.

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