BAYESIAN UNIT-ROOT TESTING INSTOCHASTIC VOLATILITY MODELS WITHCORRELATED ERRORS

Abstract

A series of returns are often modeled using stochastic volatility models. Many observed financial series exhibit unit-root non-stationarybehavior in the latent AR(1) volatility process and tests for a unit-rootbecome necessary, especially when the error process of the returns iscorrelated with the error terms of the AR(1) process. In this paper, wedevelop a class of priors that assigns positive prior probability on thenon-stationary region, employ credible interval for the test, and showthat Markov Chain Monte Carlo methods can be implemented usingstandard software. Several practical scenarios and real examples areexplored to investigate the performance of our method.

Keywords

• Contemporaneous financial correlation, Markov chain Monte Carlo, Gibbssampling, unit-root test, WinBUGS, financial data2000 AMS Classification:62M10, 62P20

BAYESIAN UNIT-ROOT TESTING INSTOCHASTIC VOLATILITY MODELS WITHCORRELATED ERRORS

Abstract

-

Keywords

• -

References

1. Bera, A.K. and Higgins, M.L. ARCH models: properties, estimation and testing, J. Economic Surveys 7, 305–366, 1993.
2. Bollerslev, T. and Engle, R. Common persistence in conditional variance, Econometrica 61, 167–186, 1993.
3. Bollerslev, T., Chou, R.Y. and Kroner, K.F. ARCH modeling in finance: a review of the theory and empirical evidence, J. Econometrics 52, 5–59, 1992.
4. Brooks, S.P. and Gelman, A. Alternative methods for monitoring convergence of iterative simulations, J. Comput. Graph. Stat. 7, 434–455, 1998.
5. Chib, S. Nardari, F. and Shephard, N., Markov chain Monte Carlo methods for generalized stochastic volatility models, J. Econometrics 108, 281–316, 1998.
6. Chou, R. Volatility persistence and stock valuations: Some empirical evidence using GARCH, J. Appl. Econom. 3, 279–294, 1998.
7. Fridman, M. and Harris, L. A maximum likelihood approach for non-Gaussian stochastic volatility models, J. Bus. Econom. Statist. 16, 284–291, 1998.
8. Harvey, A.C. and Shephard, N. Estimation of an asymmetric stochastic volatility model for asset returns, J. Bus. Econom. Statist. 14, 429–434, 1996.

9. Jacquier, E., Polson, N.G. and Rossi, P.E. Bayesian analysis of stochastic volatility models, J. Bus. Econom. Statist. 12, 14–18, 1994.
10. Jacquier, E., Polson, N.G. and Rossi, P.E. Bayesian analysis of stochastic volatility models with fat-tails and correlated errors, J. Econometrics 122, 185–212, 2004.
11. Johannes, M. and Polson, N.G. MCMC Methods for Financial Econometrics, Handbook of Financial Econometrics, 2004.
12. Kalaylioglu, Z. and Ghosh S. K. Bayesian unit root tests for stochastic volatility models, Statistical Methodology 6, 189–201, 2009.
13. Kim, S., Shephard, N. and Chib, S. Stochastic volatility: Likelihood inference and comparison with arch models, Rev. Econom. Stud. 65, 361–393, 1998.
14. Meyer, R. and Yu, J. BUGS for a Bayesian analysis of stochastic volatility models, Econometrics Journal 2, 198–215, 2000.
15. Nakajima, J. and Omori, Y. Leverage, heavy-tails and correlated jumps in stochastic volatility models, Comput. Stat. Data Anal. 53, 2335–2353, 2009.
16. Nelson, D. Conditional heteroskedasticity in asset pricing: a new approach, Econometrica 59, 347-370, 1991.
17. Omori, Y., Chib, S., Shephard, N. and Nakajima, J. Stochastic volatility with leverage: Fast and efficient likelihood inference, J. Econometrics 140, 425–449, 2007.
18. Phillips, P.C.B. To criticize the critics: An objective Bayesian analysis of stochastic trends, J. Appl. Econom. 6, 333–364, 1991.
19. Pindyck, R. Risk, inflation, and the stock market, Am. Econ. Rev. 74, 335–351, 1984.
20. Pindyck, R. Risk aversion and determinants of stock market behavior, Rev. Econ. Stat. 70, 183–190, 1986.
21. Poterba, J.M. and Summers, L.H. The persistence of volatility and stock market fluctuations, Am. Econ. Rev. 76, 1142–1151, 1986.
22. Sandmann, G. and Koopman, S. J. Estimation of stochastic volatility models via monte carlo maximum likelihood, J. Econometrics 87, 271–301, 1988.
23. So, M. K. P. and Li, W. K. Bayesian unit-root testing in stochastic volatility models, J. Bus. Econom. Statist. 17, 491–496, 1999.
24. Yu, J. On leverage in a stochastic volatility model, J. Econometrics 127, 165–178, 2005.