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Bayesian analysis of heavy-tailed market microstructure model and its application in stock markets

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  • Xi, Yanhui
  • Peng, Hui
  • Qin, Yemei
  • Xie, Wenbiao
  • Chen, Xiaohong

Abstract

The market microstructure (MM) models using normal distribution are useful tools for modeling financial time series, but they cannot explain essential characteristics of skewness and heavy tails, which may occur in a market. To cope with this problem, a heavy-tailed market microstructure model based on Student-t distribution (MM-t) is proposed in this paper. Under the assumption of non-normality, an efficient Markov chain Monte Carlo (MCMC) method is developed for parameter estimation of the proposed model. The simulation study verifies the effectiveness of the estimation approach. In empirical study, the proposed model for various stock market indices is compared to the MM models with other distributions, such as the normal distribution and a mixture of two normal distributions. Empirical results indicate that the stock prices/returns have heavy tails and the MM-t model provides a better fit than the MM models with other distributions for some financial time series. Comparison of some different type models is also done, which demonstrates that the MM-t model fits the three indices better than the stochastic volatility (SV-t) model with Student-t distribution.

Suggested Citation

  • Xi, Yanhui & Peng, Hui & Qin, Yemei & Xie, Wenbiao & Chen, Xiaohong, 2015. "Bayesian analysis of heavy-tailed market microstructure model and its application in stock markets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 117(C), pages 141-153.
    • Handle: RePEc:eee:matcom:v:117:y:2015:i:c:p:141-153
    DOI: 10.1016/j.matcom.2015.06.006
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    1. Watanabe, Toshiaki, 2003. "Measuring Business Cycle Turning Points in Japan with a Dynamic Markov Switching Factor Model," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 21(1), pages 35-68, February.
    2. Nakajima, Jouchi & Omori, Yasuhiro, 2009. "Leverage, heavy-tails and correlated jumps in stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2335-2353, April.
    3. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    4. Reinganum, Marc R., 1990. "Market microstructure and asset pricing : An empirical investigation of NYSE and NASDAQ securities," Journal of Financial Economics, Elsevier, vol. 28(1-2), pages 127-147.
    5. Abanto-Valle, C.A. & Bandyopadhyay, D. & Lachos, V.H. & Enriquez, I., 2010. "Robust Bayesian analysis of heavy-tailed stochastic volatility models using scale mixtures of normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2883-2898, December.
    6. Friedman, Moshe & Harris, Lawrence, 1998. "A Maximum Likelihood Approach for Non-Gaussian Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 284-291, July.
    7. Asai, Manabu, 2009. "Bayesian analysis of stochastic volatility models with mixture-of-normal distributions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2579-2596.
    8. Roman Liesenfeld & Robert C. Jung, 2000. "Stochastic volatility models: conditional normality versus heavy-tailed distributions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(2), pages 137-160.
    9. Carol Alexandra & Emese Lazar, 2004. "The Equity Index Skew, Market Crashes and Asymmetric Normal Mixture GARCH," ICMA Centre Discussion Papers in Finance icma-dp2004-13, Henley Business School, University of Reading.
    10. Ausin, Maria Concepcion & Galeano, Pedro, 2007. "Bayesian estimation of the Gaussian mixture GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2636-2652, February.
    11. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    12. N. Balakrishna & Bovas Abraham & Ranjini Sivakumar, 2006. "Gamma stochastic volatility models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(3), pages 153-171.
    13. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    14. Amihud, Yakov & Mendelson, Haim, 1986. "Asset pricing and the bid-ask spread," Journal of Financial Economics, Elsevier, vol. 17(2), pages 223-249, December.
    15. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    16. Emese Lazar & Carol Alexander, 2006. "Normal mixture GARCH(1,1): applications to exchange rate modelling," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 307-336.
    17. Jun Yu & Renate Meyer, 2006. "Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 361-384.
    18. Bai, Xuezheng & Russell, Jeffrey R. & Tiao, George C., 2003. "Kurtosis of GARCH and stochastic volatility models with non-normal innovations," Journal of Econometrics, Elsevier, vol. 114(2), pages 349-360, June.
    19. Omori, Yasuhiro & Chib, Siddhartha & Shephard, Neil & Nakajima, Jouchi, 2007. "Stochastic volatility with leverage: Fast and efficient likelihood inference," Journal of Econometrics, Elsevier, vol. 140(2), pages 425-449, October.
    20. Cappuccio Nunzio & Lubian Diego & Raggi Davide, 2004. "MCMC Bayesian Estimation of a Skew-GED Stochastic Volatility Model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-31, May.
    21. Watanabe, Toshiaki, 1999. "A Non-linear Filtering Approach to Stochastic Volatility Models with an Application to Daily Stock Returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(2), pages 101-121, March-Apr.
    22. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-417, October.
    23. Markus Haas, 2004. "Mixed Normal Conditional Heteroskedasticity," Journal of Financial Econometrics, Oxford University Press, vol. 2(2), pages 211-250.
    24. Jean-Philippe Bouchaud & Rama Cont, 1998. "A Langevin approach to stock market fluctuations and crashes," Science & Finance (CFM) working paper archive 500027, Science & Finance, Capital Fund Management.
    25. Renate Meyer & Jun Yu, 2000. "BUGS for a Bayesian analysis of stochastic volatility models," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 198-215.
    26. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    27. Berg, Andreas & Meyer, Renate & Yu, Jun, 2004. "Deviance Information Criterion for Comparing Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 107-120, January.
    28. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June.
    29. C. S. Wong & W. S. Chan & P. L. Kam, 2009. "A Student t-mixture autoregressive model with applications to heavy-tailed financial data," Biometrika, Biometrika Trust, vol. 96(3), pages 751-760.
    30. Asai, Manabu, 2008. "Autoregressive stochastic volatility models with heavy-tailed distributions: A comparison with multifactor volatility models," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 332-341, March.
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