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Testing for Non-Linear Structure in an Artificial Financial Market

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  • Shu-Heng Chen
  • Thomas Lux
  • Michele Marchesi

Abstract

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.

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Bibliographic Info

Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 447.

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Length: pages
Date of creation: Feb 1999
Date of revision:
Handle: RePEc:bon:bonsfb:447

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Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 6884
Web page: http://www.bgse.uni-bonn.de

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Keywords: artificial financial market; chaos; non-linearity; ARCH models;

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References

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  1. William Barnett & A. Ronald Gallant & Melvin J. Hinich & Jochen A. Jungeilges & Daniel T. Kaplan & Mark J. Jensen, 2012. "A Single-Blind Controlled Competition Among Tests For Nonlinearity And Chaos," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201219, University of Kansas, Department of Economics, revised Sep 2012.
  2. Ching-Wei Tan, 1999. "Estimating the Complexity Function of Financial Time Series: An Estimation Based on Predictive Stochastic Complexity," Computing in Economics and Finance 1999 1143, Society for Computational Economics.
  3. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-96, July.
  4. Day, R. & Huang, W., 1988. "Bulls, Bears And Market Sheep," Papers m8822, Southern California - Department of Economics.
  5. Lux, Thomas, 1998. "The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(2), pages 143-165, January.
  6. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
  7. Medio,Alfredo & Gallo,Giampaolo, 1995. "Chaotic Dynamics," Cambridge Books, Cambridge University Press, number 9780521484619, October.
  8. Gilmore, Claire G., 1993. "A new test for chaos," Journal of Economic Behavior & Organization, Elsevier, vol. 22(2), pages 209-237, October.
  9. Youssefmir, Michael & Huberman, Bernardo A., 1997. "Clustered volatility in multiagent dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 32(1), pages 101-118, January.
  10. De Vries, C.G. & Leuven, K.U., 1994. "Stylized Facts of Nominal Exchange Rate Returns," Papers 94-002, Purdue University, Krannert School of Management - Center for International Business Education and Research (CIBER).
  11. Frank, Murray & Stengos, Thanasis, 1989. "Measuring the Strangeness of Gold and Silver Rates of Return," Review of Economic Studies, Wiley Blackwell, vol. 56(4), pages 553-67, October.
  12. Lux, Thomas, 1997. "Time variation of second moments from a noise trader/infection model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(1), pages 1-38, November.
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