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I think you're just spouting a lot of buzzwords, and you're actually conflating (a) the relevance of chaos theory and (b) criticisms of normal distributions in
by thetwiceler 13y ago
I think you're just spouting a lot of buzzwords, and you're actually conflating (a) the relevance of chaos theory and (b) criticisms of normal distributions in economics.
A major recent criticism is of some economic models which have assumptions to the effect of "returns on this investment will be normally distributed." The criticism is that evidence seems to suggest that returns are not actually normally distributed; rather they have "fat tails," meaning that extreme events are more likely than with a normal distribution. And this error causes economic models to discount the role of these unlikely extreme events.
The Black-Scholes model effectively models stock prices as Brownian motion. This boils down to a single assumption: stock prices are the buildup of lots of very small INDEPENDENT random events (with FINITE variance) that occur over short times periods; this leads straight to Brownian motion. Brownian motion is indeed continuous; however, it is nowhere differentiable with probability 1. Because of the assumptions of finite variance and independence, the CLT tells us that returns will be normally distributed. So here, people pretty much agree that it's always these assumptions of independence that cause these models to predict poorly.
This is totally different from chaos theory. First of all, chaotic systems are not necessarily complex. Here's a chaotic map with a "nice little formula":
f : [0,1) -> [0,1)
f(x) = 2*x (mod 1)
While this is chaotic, we can understand much about this map. For example, each application produces an entropy of 1 bit (see entropy of dynamical systems...). So this is a map that "produces randomness" in a way. This is philosophically nice, because probability theory itself doesn't at all explain how randomness comes about.
- JDDunn9 13y agoYou can create a chaotic map with a simple formula, but those don't appear often in the real world. Give me the formula for the weather, or to predict the next earthquake, or to model turbulence. If the stock market movements were normally distributed, crashes would be extremely rare. Something like 1 every 10,000 years. Virtually all economic models assume something to be true that we know isn't.
- thetwiceler 13y agoOnce again, don't confuse predictability with ability to understand a system. We actually have a fairly good understanding of weather dynamics and turbulence - and I can give you the formula for both of these - the Navier-Stokes equation! Not the simplest equation, but something understandable (yes, I know there's a Millenium Prize problem to see if we always get a smooth solution). We do understand how turbulence arises from this. And we understand the weather very well. However, we can't predict the weather, nor can we predict the earthquakes. And as you correctly point out, the reason for this is chaos. The reason is not that we don't understand the underlying processes that govern these dynamics. Rather, the uncertainties in our initial conditions increase exponentially with time (due to chaos) and make long-term predictions unreliable.