Bayesian Testing for Asset Volatility Persistence on Multivariate Stochastic Volatility Models

Yong Li, Fang-Ping Peng, Hao-Feng Xu

Sun Yat-sen Business School, Sun Yat-sen University, Guangzhou, China.

DOI: 10.4236/jmf.2012.21010                

Abstract

In empirical finance, it is well-known that the volatility of asset returns is highly persistent. The persistence of the volatility process may be checked by testing for a unit root on stochastic volatility models. In this paper, a Bayesian test statistic based on decision theory is developed for testing a unit root on multivariate stochastic volatility models. At last, the developed approach is applied to investigate the persistent effect of financial crisis on the two main stock markets in China.

Keywords

Asset Volatility Persistency; Bayes Factor; Decision Theory; Markov Chain Monte Carlo; Unit Root Testing; Multivariate Stochastic Volatility Models

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	R. Y. Chou, “Volatility Persistence and Stock Valuation: Some Em-pirical Evidence Using GARCH,” Journal of Applied Econometrics, Vol. 3, No. 4, 1988, pp. 279-294. doi:10.1002/jae.3950030404
[2]	J. Wright, “Testing a Unit Root in the Volatility of Asset Returns,” Journal of Applied Econometrics, Vol. 14, No. 3, 1999, pp. 309-318. doi:10.1002/(SICI)1099-1255(199905/06)14:3<309::AID-JAE531>3.0.CO;2-X
[3]	D. Berger, A. Chaboud and E. Hjalmarsson, “What Drives Volatility Persistence in the Foreign Exchange Market,” Journal of Financial Economics, Vol. 94, No. 2, 2009, pp. 192-213. doi:10.1016/j.jfineco.2008.10.006
[4]	B. T. Ewing and F. Malik, “Estimating Volatility Persistence in Oil Prices under Structural Breaks,” The Financial Review, Vol. 45, No. 4, 2010, pp. 1011-1023. doi:10.1111/j.1540-6288.2010.00283.x
[5]	T. Bollerslev and R. F. Engle, “Common Persistence in Conditional Variance,” Econometrica, Vol. 61, No. 1, 1993, pp. 167-186. doi:10.2307/2951782
[6]	N. Shephard, “Stochastic Volatility: Selected Reading,” Oxford University Press, Oxford, 2005.
[7]	M. K. P. So and W. K. Li, “Bayesian Unit-Root Testing in Stochastic Volatility Models,” Journal of Business and Economic Statistics, Vol. 17, No. 4, 1999, pp. 491-496. doi:10.2307/1392407
[8]	R. E. Kass and A. E. Raftery, “Bayes Factor,” Journal of the Americana Statistical Association, Vol. 90, No. 430, 1995, pp. 773-795. doi:10.2307/2291091
[9]	S. Chib, “Marginal Likelihood from the Gibbs Output,” Journal of the American Statistical Association, Vol. 90, No. 432, 1995, pp. 1313-1321. doi:10.2307/2291521
[10]	Y. Li and J. Yu, “A New Bayesian Unit Root Test in Stochastic Volatility Models,” Research Collection School of Economics, Paper 1240, 2010.
[11]	Y. Li, Z. X. Ni and J. Zhang, “An Efficient Stochastic Si- mulation Algorithm for Bayesian Unit Root Testing in Stochastic Volatility Models,” Computational Economics, Vol. 37, No. 3, 2011, pp. 237-248. doi:10.1007/s10614-011-9252-4
[12]	Y. Li and J. Yu, “Bayes-ian Hypothesis Testing in Latent Variable Models,” Journal of Econometrics, Vol. 166, No. 2, 2012, pp. 237-246. doi:10.1016/j.jeconom.2011.09.040
[13]	J. Zhang, Y. Li and J. Zhang, “Bayesian Testing a Unit Root in the Volatility of Asset Returns: An Empirical Com- parison,” Working Paper, 2011.
[14]	M. Asai, M. AcAleer and J. Yu, “Multivariate Stochastic Volatility Models: A Review,” Econometric Review, Vol. 25, No. 2-3, 2006, pp. 145-175. doi:10.1080/07474930600713564
[15]	A. C. Harvey, E. Ruiz and E. Shephard, “Multivariate Stochastic Variance Models,” Review of Economic Studies, Vol. 61, No. 2, 1994, pp. 247-264. doi:10.2307/2297980
[16]	J. Yu and R. Meyer, “Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison,” Econometric Review, Vol. 25, No. 2-3, 2006, pp. 361-384. doi:10.1080/07474930600713465
[17]	T. A. Tanner and W. H. Wong, “The Calculation of Posterior Distributions by Data Augmentation,” Journal of the American Statistical Association, Vol. 82, No. 398, 1987, pp. 528-549. doi:10.2307/2289457
[18]	D. J. Spiegelhalter, A. Thomas, N. G. Best and D. Lunn, “Win-BUGS User Manual. Version 1.4,” MRC Biostatistics Unit, Cambridge, 2003.