## Tuesday, October 6, 2009

### When you're strange Faces come out of the rain

Anonymous Monetarist: Tonight we are pleased to have Dimitris N.Chorafas who comes to us via his book Chaos Theory in Financial Markets, published in 1994.

Dimitris: Thanks. Nice to be here.

What is Chaos Theory?

Henri Poincare realized that if a system consisted of a few parts that interacted strongly, it could exhibit unpredictable behavior. This concept is at the origin of chaos theory. The object of chaos theory is to study the irregular behavior of simple deterministic equations by providing more sophisticated tools that are closer to real life.

Change and order are essential, though they are contradictory to each other. Their incompatibility is best expressed through modes of complexity that account for phenomena that, at first sight, don't even seem to fit together.

How so?

Chaotic systems are essentially periodic. What makes them appear random is a continual transition from one periodic orbit to another.

In the past, the perceived state of randomness was thought to be due to chance. However given the strangeness of math we can show that chaos affects any system that has some sort of sensitive dependence on an initial condition. Any small change or uncertainty in conditions at a starting point will eventually make predictions about the system and its behavior extremely difficult if not impossible.

How does one adjust for this?

The point many people trained in traditional financial analysis fail to appreciate is that discontinuous changes requires a sort of discontinuous thinking. Because of its upside down characteristics, discontinuous thinking has never been popular with the upholders of continuity and the status quo- nor with mathematicians tied to classical theories.

Discontinuous thinking is an invitation to consider the unlikely, if not the absurd.

Nothing should be dismissed out of hand in a time of transition from stability to chaos - and vice versa-when discontinuities, not equilibria, are the rule.

What do you see as the principal failings of classical theories?

Classical econometric analysis assumes that if there are no outside or exogenous influences, the system is at rest. Internal or endogenous factors are thought to balance out. This rests on the hypothesis that supply equals demand and therefore an efficient market comes to play.

And this is not the case?

Nothing could be further from the truth. Both endogenous and exogneous factors can shift a financial system from equilibrium. As the market reacts, it moves from the stable conditions associated with order and tidiness. Disequilibria rather than equilibria are the characteristic properties. Living systems behave that way.

Would you consider the markets to be a living system? If so would you view government intervention as a hazard?

Yes, financial markets are dynamic, evolving structures and do not repsond kindly to attempts to control an economy and keep it at equilibrium, no matter how good the intentions may be. Even at the foundations of efficient market hypothesis, a lack of dynamic movement takes the life out of the system.

Since the characteristic of free capital markets is dynamic behavior, we need models able to represent- without undue simplification- disorderly systems that move by fits and starts. Underlying turbulence is flow, which involves shape and change as well as motion and form. Complex systems are not inherently efficient. Instead they can give rise to turbulence and coherence at the same time. Turbulence in fluids might have something to do with an infinitely tangled solution space, which David Ruelle calls strange attractor.

What is a strange attractor?

A strange attractor is a mathematical portrait of order within a chaotic environment. It is a solution space that traces the behavior of a complex system over time, revealing how it is attracted to an ideal state - essentially revolving around it.

Is there a simple analogy?

We can look at this from a flow dynamics perspective. In flow dynamics we assume that change in systems reflects some reality independent of a particular instant. It is like seeing liquid penetrating a liquid or as another example, a solid growing crystals. Both create a state of turbulence,and we are interested in the shape.

We can look at this from an information technology viewpoint.

As a system becomes chaotic , it generates a steady stream of information. Because of its unpredictability, each new observation is a new entry. The channel transmitting the information upward is a strange attractor. In the domain of strange attractors, initial small uncertainties are magnified into large patterns. Their initial condition might have been due to randomess.

Making predictions under these conditions is as if we are trying to guess the evolution of shape in space and time.

How is this of practical importance?

We can think of flows in many ways, including flows in economic and finance.

At first ,such flows may be linear. Then they can bifuractate to a complex state. Subsequently , they oscillate. Finally, they may be chaotic. Flow dynamics are characterized by a universality of shapes with similarities and dissimilarities across scales. Flows within flows are part and parcel of dynamic systems in market dynamics, among other domains.

So strange attractors represent a picture of reality's order flow?

Uh ... yes. Financial analysts who understand chaos theory look at strange attractors as engines of information. Their domain is characterized by both order and disorder. Order does in fact arise out of complex behavioral processes, through successive transitions.

A happy ending?

Chaos theory aims to represent these transitions for dynamic systems with simple attractors, the solution space may contain in its behavior sufficient information to make chaos predictable.

Thanks Dimitris.

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