SFB 303 Discussion Paper No. B - 447
Shu-Heng, Thomas Lux and Michele Marchesi
Title: Testing for Non-Linear Structure in an Artificial Financial Market
We present a stochastic simulation model of a prototype financial market.
Our market is populated by both noise traders and fundamentalist
speculators. The dynamics covers switches in the prevailing mood among noise
traders (optimistic or pessimistic) as well as switches of agents between
the noise traders and fundamentalist group in response to observed
differences in profits. The particular behavioral variant adopted by an
agent also determines her decision to enter on the long or the short side of
the market. Short-run imbalances between demand and supply lead to price
adjustments by a market maker or auctioneer in the usual Walrasian manner.
Our interest in this paper is in exploring the behavior of the model when
testing for the presence of chaos or non-linearity in the simulated data.
First, attempts to determine the fractal dimension of the underlying process
give unsatisfactory results in that we experience a lack of convergence of
the estimate. Explicit tests for non-linearity and dependence (the BDS and
Kaplan tests) also give very unstable results in that both acceptance and
strong rejection of IIDness can be found in different realizations of our
model. All in all, this behavior is very similar to experience collected
with empirical data and our results may point towards an explanation of why
robustness of inference in this area is low. However, when testing for
dependence in second moments and estimating GARCH models, the results appear
much more robust and the chosen GARCH specification closely resembles the
typical outcome of empirical studies.
Keywords: artificial financial market, chaos, non-linearity, ARCH models
JEL-Classification-Number: C14, D84, G12
Creation-Date: Febuary 1999
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