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Testing of a market fraction model and power-law behaviour in the DAX 30

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  • He, Xue-Zhong
  • Li, Youwei

Abstract

This paper tests a simple market fraction asset pricing model with heterogeneous agents. By selecting a set of structural parameters of the model through a systematic procedure, we show that the autocorrelations (of returns, absolute returns and squared returns) of the market fraction model share the same pattern as those of the DAX 30. By conducting econometric analysis via Monte Carlo simulations, we characterize these power-law behaviours and find that estimates of the power-law decay indices, the (FI)GARCH parameters, and the tail index of the selected market fraction model closely match those of the DAX 30. The results strongly support the explanatory power of the heterogeneous agent models.

Suggested Citation

  • He, Xue-Zhong & Li, Youwei, 2015. "Testing of a market fraction model and power-law behaviour in the DAX 30," Journal of Empirical Finance, Elsevier, vol. 31(C), pages 1-17.
    • Handle: RePEc:eee:empfin:v:31:y:2015:i:c:p:1-17
    DOI: 10.1016/j.jempfin.2015.01.001
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    Cited by:

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    2. Xue-Zhong He & Youwei Li, 2017. "The adaptiveness in stock markets: testing the stylized facts in the DAX 30," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 1071-1094, November.
    3. Vygintas Gontis & Shlomo Havlin & Aleksejus Kononovicius & Boris Podobnik & H. Eugene Stanley, 2015. "Stochastic model of financial markets reproducing scaling and memory in volatility return intervals," Papers 1507.05203, arXiv.org, revised Oct 2016.
    4. Vygintas Gontis & Aleksejus Kononovicius, 2017. "The consentaneous model of the financial markets exhibiting spurious nature of long-range memory," Papers 1712.05121, arXiv.org, revised Feb 2018.
    5. He, Xue-Zhong & Li, Kai & Santi, Caterina & Shi, Lei, 2022. "Social interaction, volatility clustering, and momentum," Journal of Economic Behavior & Organization, Elsevier, vol. 203(C), pages 125-149.
    6. He, Xue-Zhong & Zheng, Huanhuan, 2016. "Trading heterogeneity under information uncertainty," Journal of Economic Behavior & Organization, Elsevier, vol. 130(C), pages 64-80.
    7. He, Xue-Zhong & Li, Youwei & Zheng, Min, 2019. "Heterogeneous agent models in financial markets: A nonlinear dynamics approach," International Review of Financial Analysis, Elsevier, vol. 62(C), pages 135-149.
    8. Guillaume Coqueret, 2017. "Empirical properties of a heterogeneous agent model in large dimensions," Post-Print hal-02000726, HAL.
    9. He, Xue-Zhong & Li, Kai & Wang, Chuncheng, 2016. "Volatility clustering: A nonlinear theoretical approach," Journal of Economic Behavior & Organization, Elsevier, vol. 130(C), pages 274-297.
    10. Coqueret, Guillaume, 2017. "Empirical properties of a heterogeneous agent model in large dimensions," Journal of Economic Dynamics and Control, Elsevier, vol. 77(C), pages 180-201.
    11. Zheng, Min & Liu, Ruipeng & Li, Youwei, 2018. "Long memory in financial markets: A heterogeneous agent model perspective," International Review of Financial Analysis, Elsevier, vol. 58(C), pages 38-51.
    12. Zhong-Qiang Zhou & Jie Li & Wei Zhang & Xiong Xiong, 2022. "Government intervention model based on behavioral heterogeneity for China’s stock market," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-19, December.
    13. Gontis, V. & Havlin, S. & Kononovicius, A. & Podobnik, B. & Stanley, H.E., 2016. "Stochastic model of financial markets reproducing scaling and memory in volatility return intervals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1091-1102.
    14. Lux, Thomas & Alfarano, Simone, 2016. "Financial power laws: Empirical evidence, models, and mechanisms," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 3-18.
    15. Chen, Zhenxi & Zheng, Huanhuan, 2022. "Herding in the Chinese and US stock markets: Evidence from a micro-founded approach," International Review of Economics & Finance, Elsevier, vol. 78(C), pages 597-604.
    16. Gontis, V. & Kononovicius, A., 2018. "The consentaneous model of the financial markets exhibiting spurious nature of long-range memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 1075-1083.
    17. Zheng, Min & Wang, Hefei & Wang, Chengzhang & Wang, Shouyang, 2017. "Speculative behavior in a housing market: Boom and bust," Economic Modelling, Elsevier, vol. 61(C), pages 50-64.
    18. Goldbaum, David, 2017. "Divergent Behavior in Markets with Idiosyncratic Private Information," Review of Behavioral Economics, now publishers, vol. 4(2), pages 181-213, September.
    19. Guillaume Coqueret, 2016. "Empirical properties of a heterogeneous agent model in large dimensions," Post-Print hal-02088097, HAL.
    20. Giovanni Campisi & Silvia Muzzioli, 2020. "Fundamentalists heterogeneity and the role of the sentiment indicator," Department of Economics 0167, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".

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    Keywords

    Asset pricing; Fundamentalists and trend followers; (FI)GARCH; Power-law; Tail index;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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