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Unit Root Hypothesis in the Presence of Stochastic Volatility, a Bayesian Analysis

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  • Jin-Yu Zhang
  • Yong Li

    ()

  • Zhu-Ming Chen

Abstract

This paper investigates the impact of stochastic volatility on the Dickey–Fuller unit root test. Monte Carlo simulations show that the test size is seriously distorted if nonstationary stochastic volatility is ignored. To improve the performance of the test, we propose a Bayesian test for unit root that is robust in the presence of stationary and nonstationary stochastic volatility. The finite sample property of the proposed test statistic is evaluated using Monte Carlo studies. Applying the developed method, we test the policy effect of the Split Share Structure Reform, which is an important milestone for the development of the emerging stock market in China. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Jin-Yu Zhang & Yong Li & Zhu-Ming Chen, 2013. "Unit Root Hypothesis in the Presence of Stochastic Volatility, a Bayesian Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 41(1), pages 89-100, January.
    • Handle: RePEc:kap:compec:v:41:y:2013:i:1:p:89-100
    DOI: 10.1007/s10614-012-9319-x
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    References listed on IDEAS

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    1. Yong Li & Zhongxin Ni & Jie Zhang, 2011. "An Efficient Stochastic Simulation Algorithm for Bayesian Unit Root Testing in Stochastic Volatility Models," Computational Economics, Springer;Society for Computational Economics, vol. 37(3), pages 237-248, March.
    2. Phillips, P C B, 1991. "Bayesian Routes and Unit Roots: De Rebus Prioribus Semper Est Disputandum," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 435-473, Oct.-Dec..
    3. Kim, Kiwhan & Schmidt, Peter, 1993. "Unit root tests with conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 59(3), pages 287-300, October.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. So, Mike K P & Li, W K, 1999. "Bayesian Unit-Root Testing in Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(4), pages 491-496, October.
    6. Andersen, Torben G. & Chung, Hyung-Jin & Sorensen, Bent E., 1999. "Efficient method of moments estimation of a stochastic volatility model: A Monte Carlo study," Journal of Econometrics, Elsevier, vol. 91(1), pages 61-87, July.
    7. Ling, Shiqing & Li, W.K., 2003. "Asymptotic Inference For Unit Root Processes With Garch(1,1) Errors," Econometric Theory, Cambridge University Press, vol. 19(4), pages 541-564, August.
    8. 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.
    9. Li, Yong & Yu, Jun, 2012. "Bayesian hypothesis testing in latent variable models," Journal of Econometrics, Elsevier, vol. 166(2), pages 237-246.
    10. 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.
    11. Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 183-204, April.
    12. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

    1. Cathy W. S. Chen & Sangyeol Lee & Shu-Yu Chen, 2016. "Local non-stationarity test in mean for Markov switching GARCH models: an approximate Bayesian approach," Computational Statistics, Springer, vol. 31(1), pages 1-24, March.
    2. Pan, Qi & Li, Yong, 2013. "Testing volatility persistence on Markov switching stochastic volatility models," Economic Modelling, Elsevier, vol. 35(C), pages 45-50.
    3. Thomas Nanfeng Li & Agnès Tourin, 2016. "Optimal pairs trading with time-varying volatility," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 1-29, September.
    4. Xiao-Bin Liu & Yong Li, 2013. "Bayesian testing volatility persistence in stochastic volatility models with jumps," Quantitative Finance, Taylor & Francis Journals, vol. 14(8), pages 1415-1426, December.

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