Wolfram Science Group
Phoenix, AZ USA
Registered: Aug 2003
One of the promising ideas mentioned in the paper is modeling diverse endogeneous expectations or popular models of a price series, an idea put forward by R.J. Shiller among others. That is, one partitions market participants into some number of classes based on the sort of model they are posited to have of the economic process.
Then they react to price changes according to their model. Composite expectations change as different segments of the population react to the same developments differently. Traditionally this sort of model has been examined with continuous variables, essentially tracking a few feedback loops, an easy way to get "excess volatility" compared to the amount of new information fundamentals are providing, to get trending and boom bust cycles, etc.
Noticing that price data exhibits some signs of power laws rather than normal distributions gave rise to a different approach, more along the lines of Da Silva et al, trying to find a version of statistics that properly characterizes the mix of trending, mean reversion, long tails, large shocks, etc seen in real financial data.
One approach would be just to use NKS systems to generate various series and look for ones that exhibit similar statistical "signatures" (both directly, and in linear combinations). Another, though, would be to build intuitive assumptions about classes of popular models into an NKS system, and then look at the sort of statistics that model produces. One might call these "search" and "construction". I think in the end we will need both, to see where the sort of empirical statistics we see may actually be coming from.
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