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Statistical Properties of a Heterogeneous Asset Price Model with Time-Varying Second Moment

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Author Info
Carl Chiarella () (School of Finance and Economics, University of Technology, Sydney)
Xue-Zhong He () (School of Finance and Economics, University of Technology, Sydney)
Duo Wang

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Abstract

Stability and bifurcation analysis of deterministic systems has been widely used in modeling financial markets. However, the impact of such dynamic phenomena on various statistical properties of the corresponding stochastic model, including skewness and excess kurtosis, various autocorrelation (AC) patterns of under and over reactions, and volatility clustering characterised by the long-range dependence of ACs, is not clear and has been very little studied. This paper aims to study this issue. Through a simple behavioural asset pricing model with fundamentalists and chartists, we examine the statistical properties of the model and their connection to the dynamics of the underlying deterministic model. In particular, our analysis leads to some insights into the type of mechanism that may be generating some of the stylised facts, such as fat tails, skewness, high kurtosis and long memory, observed in high frequency financial data.

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Publisher Info
Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 142.

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Length: 14
Date of creation: 01 Nov 2004
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Handle: RePEc:uts:rpaper:142

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Related research
Keywords: fundamentalists; chartists; stability; bifurcation; investors' under- and over-reactions; stylized facts;

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Find related papers by JEL classification:
D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
E21 - Macroeconomics and Monetary Economics - - Macroeconomics: Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
C60 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - General

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  1. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August. [Downloadable!] (restricted)
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    Other versions:
  5. Chiarella, Carl & He, Xue-Zhong, 2002. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model," Computational Economics, Springer, vol. 19(1), pages 95-132, February. [Downloadable!]
    Other versions:
  6. Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, School of Finance and Economics, University of Technology, Sydney. [Downloadable!]
  7. Cars H. Hommes, 2001. "Financial Markets as Nonlinear Adaptive Evolutionary Systems," Tinbergen Institute Discussion Papers 01-014/1, Tinbergen Institute. [Downloadable!]
    Other versions:
  8. 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.
    Other versions:
  9. Hommes, C.H., 2001. "Modeling the stylized facts in finance through simple nonlinear adaptive systems," CeNDEF Working Papers 01-06, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance. [Downloadable!]
  10. Gaunersdorfer, Andrea, 2000. "Endogenous fluctuations in a simple asset pricing model with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 799-831, June. [Downloadable!] (restricted)
  11. Gaunersdorfer, A. & Hommes, C.H. & Wagener, F.O.O., 2003. "Bifurcation Routes to Volatility Clustering under Evolutionary Learning," CeNDEF Working Papers 03-03, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance. [Downloadable!]
    Other versions:
  12. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May. [Downloadable!] (restricted)
  13. Carl Chiarella & Roberto Dieci & Laura Gardini, 2001. "Speculative Behaviour and Complex Asset Price Dynamics," Research Paper Series 49, Quantitative Finance Research Centre, University of Technology, Sydney.
  14. repec:att:wimass:19976 is not listed on IDEAS
  15. Xue-Zhong (Tony) He & Carl Chiarella, 2001. "Asset Price and Wealth Dynamics under Heterogeneous Expectations," CeNDEF Workshop Papers, January 2001 5A.2, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    Other versions:
  16. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June. [Downloadable!] (restricted)
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  17. 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. [Downloadable!] (restricted)
  18. Carl Chiarella & Xue-Zhong He & Duo Wang, 2004. "A Behavioural Asset Pricing Model with a Time-Varying Second Moment," Research Paper Series 141, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  19. Bullard, James & Duffy, John, 1999. "Using Genetic Algorithms to Model the Evolution of Heterogeneous Beliefs," Computational Economics, Springer, vol. 13(1), pages 41-60, February. [Downloadable!]
    Other versions:
  20. W. Brian Arthur & John H. Holland & Blake LeBaron & Richard Palmer & Paul Taylor, 1996. "Asset Pricing Under Endogenous Expectation in an Artificial Stock Market," Working Papers 96-12-093, Santa Fe Institute.
  21. J. Doyne Farmer & Shareen Joshi, 2000. "The Price Dynamics of Common Trading Strategies," Working Papers 00-12-069, Santa Fe Institute.
    Other versions:
  22. Carl Chiarella & Xue-Zhong He, 2000. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model with a Market Maker," Research Paper Series 35, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
    Other versions:
  23. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-96, July. [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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