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A Noise Trader Model As A Generator Of Apparent Financial Power Laws And Long Memory

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Author Info
ALFARANO, SIMONE
LUX, THOMAS

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Abstract

In various agent-based models, the stylized facts of financial markets (unit roots, fat tails, and volatility clustering) have been shown to emerge from the interactions of agents. However, the complexity of these models often limits their analytical accessibility. In this paper we show that even a very simple model of a financial market with heterogeneous interacting agents is capable of reproducing these ubiquitous statistical properties. The simplicity of our approach permits us to derive some analytical insights using concepts from statistical mechanics. In our model, traders are divided into two groups, fundamentalists and chartists, and their interactions are based on a variant of the herding mechanism introduced by A. Kirman (Ants, rationality, and recruitment, Quarterly Journal of Economics 108, 137 156, 1993). The statistical analysis of simulated data points toward long-term dependence in the autocorrelations of squared and absolute returns and hyperbolic decay in the tail of the distribution of raw returns, both with estimated decay parameters in the same range as those of empirical data. Theoretical analysis, however, excludes the possibility of true scaling behavior because of the Markovian nature of the underlying process and the boundedness of returns. The model, therefore, only mimics power law behavior. Similarly to the phenomenological volatility models analyzed by LeBaron (Stochastic volatility as a simple generator of apparent financial power laws and long memory, Quantitative Finance 1, 621 631, 2001), the usual statistical tests are not able to distinguish between true and pseudo-scaling laws in the dynamics of our artificial market.

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Publisher Info
Article provided by Cambridge University Press in its journal Macroeconomic Dynamics.

Volume (Year): 11 (2007)
Issue (Month): S1 (November)
Pages: 80-101
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Handle: RePEc:cup:macdyn:v:11:y:2007:i:s1:p:80-101_06

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. P. Bak & M. Paczuski & M. Shubik, 1996. "Price Variations in a Stock Market with Many Agents," Working Papers 96-09-075, Santa Fe Institute.
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  2. Friedrich Wagner & Thomas Lux & Simone Alfarano, 2005. "Time-Variation of Higher Moments in a Financial Market with Heterogeneous Agents: An Analytical Approach," Working Papers wp05-02, Warwick Business School, Financial Econometrics Research Centre. [Downloadable!]
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  3. Lux, T. & M. Marchesi, . "Volatility Clustering in Financial Markets: A Micro-Simulation of Interacting Agents," Discussion Paper Serie B 437, University of Bonn, Germany, revised Jul 1998.
  4. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November. [Downloadable!] (restricted)
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  5. I.N. Lobato & N.E. Savin, 1996. "Real and Spurious Long Memory Properties of Stock Market Data," Econometrics 9605004, EconWPA, revised 26 Sep 1996. [Downloadable!]
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  6. Alan Kirman & Gilles Teyssière, 2002. "Microeconomic Models for Long Memory in the Volatility of Financial Time Series," Studies in Nonlinear Dynamics & Econometrics, Berkeley Electronic Press, vol. 5(4), pages 1083-1083. [Downloadable!] (restricted)
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  7. Gaunersdorfer, A. & Hommes, C.H. & Wagener, F.O.O., 2000. "Bifurcation Routes to Volatility Clustering," CeNDEF Working Papers 00-04, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
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  8. Gaunersdorfer, A. & Hommes, C.H., 2000. "A Nonlinear Structural Model for Volatility Clustering," CeNDEF Working Papers 00-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
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  9. 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).
  10. Andersson, Michael K. & Eklund, Bruno & Lyhagen, Johan, 1999. "A Simple Linear Time Series Model with Misleading Nonlinear Properties," Working Paper Series in Economics and Finance 300, Stockholm School of Economics.
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  11. Simone Alfarano & Thomas Lux, 2002. "A minimal noise trader model with realistic time series," Computing in Economics and Finance 2002 317, Society for Computational Economics.
  12. LeBaron, Blake, 2000. "Agent-based computational finance: Suggested readings and early research," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 679-702, June. [Downloadable!] (restricted)
  13. Lux, Thomas & Schornstein, Sascha, 2005. "Genetic learning as an explanation of stylized facts of foreign exchange markets," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 169-196, February. [Downloadable!] (restricted)
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  14. Kirman, Alan, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, MIT Press, vol. 108(1), pages 137-56, February. [Downloadable!] (restricted)
  15. Georges, Christophre, 2006. "Learning with misspecification in an artificial currency market," Journal of Economic Behavior & Organization, Elsevier, vol. 60(1), pages 70-84, May. [Downloadable!] (restricted)
  16. Jeffrey A. Frankel & Kenneth A. Froot, 1987. "The Dollar as an Irrational Speculative Bubble: A Tale of Fundamentalisists," NBER Working Papers 1854, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  17. Granger, Clive W. J. & Terasvirta, Timo, 1999. "A simple nonlinear time series model with misleading linear properties," Economics Letters, Elsevier, vol. 62(2), pages 161-165, February. [Downloadable!] (restricted)
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  18. Arifovic, Jasmina & Gencay, Ramazan, 2000. "Statistical properties of genetic learning in a model of exchange rate," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 981-1005, June. [Downloadable!] (restricted)
  19. Iori, Giulia, 2002. "A microsimulation of traders activity in the stock market: the role of heterogeneity, agents' interactions and trade frictions," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 269-285, October. [Downloadable!] (restricted)
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  20. Youssefmir, Michael & Huberman, Bernardo A., 1997. "Clustered volatility in multiagent dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 32(1), pages 101-118, January. [Downloadable!] (restricted)
  21. J. Doyne Farmer & Shareen Joshi, 2000. "The Price Dynamics of Common Trading Strategies," Working Papers 00-12-069, Santa Fe Institute.
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  22. Shu-Heng Chen & Thomas Lux & Michele Marchesi, 1999. "Testing for Non-Linear Structure in an Artificial Financial Market," Discussion Paper Serie B 447, University of Bonn, Germany.
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  23. Beja, Avraham & Goldman, M Barry, 1980. " On the Dynamic Behavior of Prices in Disequilibrium," Journal of Finance, American Finance Association, vol. 35(2), pages 235-48, May. [Downloadable!] (restricted)
  24. Chen, Shu-Heng & Yeh, Chia-Hsuan, 2002. "On the emergent properties of artificial stock markets: the efficient market hypothesis and the rational expectations hypothesis," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 217-239, October. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Thomas Lux, 2008. "Rational Forecasts or Social Opinion Dynamics? Identification of Interaction Effects in a Business Climate Survey," Kiel Working Papers 1424, Kiel Institute for the World Economy. [Downloadable!]
  2. Lux, Thomas, 2008. "Stochastic behavioral asset pricing models and the stylized facts," Economics Working Papers 2008,08, Christian-Albrechts-University of Kiel, Department of Economics. [Downloadable!]
  3. Lux, Thomas & Kaizoji, Taisei, 2006. "Forecasting volatility and volume in the Tokyo stock market : long memory, fractality and regime switching," Economics Working Papers 2006,13, Christian-Albrechts-University of Kiel, Department of Economics. [Downloadable!]
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  4. Lux, Thomas, 2008. "Rational forecasts or social opinion dynamics? : identification of interaction effects in a business climate survey," Economics Working Papers 2008,07, Christian-Albrechts-University of Kiel, Department of Economics. [Downloadable!]
  5. Thomas Lux, 2008. "Stochastic Behavioral Asset Pricing Models and the Stylized Facts," Kiel Working Papers 1426, Kiel Institute for the World Economy. [Downloadable!]
  6. Alfarano, Simone & Lux, Thomas & Wagner, Friedrich, 2005. "Time-variation of higher moments in a financial market with heterogeneous agents : an analytical approach," Economics Working Papers 2005,14, Christian-Albrechts-University of Kiel, Department of Economics. [Downloadable!]
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