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A New Bayesian Unit Root Test in Stochastic Volatility Models

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Author Info

  • Yong Li

    (Sun Yat-Sen University)

  • Jun Yu

    ()
    (Sim Kee Boon Institute for Financial Economics, School of Economics and Lee Kong Chian School of Business)

Abstract

A new posterior odds analysis is proposed to test for a unit root in volatility dynamics in the context of stochastic volatility models. Our analysis extends the Bayesian unit root test of So and Li (1999, Journal of Business and Economic Statistics) in the two important ways. First, a numerically more stable algorithm is introduced to compute Bayes factors, taking into account the special structure of the competing models. Owing to its numerical stability, the algorithm overcomes the problem of the diverging “size” in the marginal likelihood approach. Second, to improve the “power” of the unit root test, a mixed prior specification with random weights is employed. It is shown that the posterior odds ratio is the by-product of Bayesian estimation and can be easily computed by MCMC methods. A simulation study examines the “size” and “power” performances of the new method. An empirical study, based on time series data covering the subprime crisis, reveals some interesting results.

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Bibliographic Info

Paper provided by Singapore Management University, School of Economics in its series Working Papers with number 14-2012.

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Length: 26 pages
Date of creation: Jan 2012
Date of revision:
Publication status: Published in SMU Economics and Statistics Working Paper Series
Handle: RePEc:siu:wpaper:14-2012

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Keywords: Bayes factor; Mixed Prior; Markov Chain Monte Carlo; Posterior odds ratio; Stochastic volatility models; Unit root testing.;

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References

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  1. Perron, P. & Ng, S., 1994. "Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties," Cahiers de recherche 9427, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 361-93, July.
  3. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-61, January.
  4. Peter C.B. Phillips, 1991. "Bayesian Routes and Unit Roots: de rebus prioribus semper est disputandum," Cowles Foundation Discussion Papers 986, Cowles Foundation for Research in Economics, Yale University.
  5. Jun Yu & Renate Meyer, 2004. "Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison," Working Papers 23-2004, Singapore Management University, School of Economics.
  6. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  7. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
  8. Chou, Ray Yeutien, 1988. "Volatility Persistence and Stock Valuations: Some Empirical Evidence Using Garch," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(4), pages 279-94, October-D.
  9. Schwert, G William, 1989. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(2), pages 147-59, April.
  10. Sims, Christopher A., 1988. "Bayesian skepticism on unit root econometrics," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 463-474.
  11. 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.
  12. 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 107-20, January.
  13. Sibylle Sturtz & Uwe Ligges & Andrew Gelman, . "R2WinBUGS: A Package for Running WinBUGS from R," Journal of Statistical Software, American Statistical Association, vol. 12(i03).
  14. 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.
  15. 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.
  16. Francis W. Ahking, 2004. "The Power of the "Objective" Bayesian Unit-Root Test," Working papers 2004-14, University of Connecticut, Department of Economics.
  17. Schotman, Peter & van Dijk, Herman K., 1991. "A Bayesian analysis of the unit root in real exchange rates," Journal of Econometrics, Elsevier, vol. 49(1-2), pages 195-238.
  18. John Geweke, 2007. "Bayesian Model Comparison and Validation," American Economic Review, American Economic Association, vol. 97(2), pages 60-64, May.
  19. Wright, Jonathan H, 1999. "Testing for a Unit Root in the Volatility of Asset Returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(3), pages 309-18, May-June.
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Cited by:
  1. Cathy Chen & Shu-Yu Chen & Sangyeol Lee, 2013. "Bayesian Unit Root Test in Double Threshold Heteroskedastic Models," Computational Economics, Society for Computational Economics, vol. 42(4), pages 471-490, December.

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