Multivariate Stochastic Volatility: A Review
Authors:
Manabu Asai a;
Michael McAleer b;
Jun Yu c
| Affiliations: | a Faculty of Economics, Soka University, Tokyo, Japan |
| b School of Economics and Commerce, University of Western Australia, Perth, Australia | |
| c School of Economics and Social Sciences, Singapore Management University, Singapore |
DOI:
10.1080/07474930600713564
Publication Frequency:
6 issues per year
Formats available:
HTML
(English)
:
PDF
(English)
You have:
FREE ACCESS
References
- 1. Aguilar, O. and West, M. (2000) Bayesian dynamic factor models and portfolio allocation. Journal of Business and Economic Statistics 18 , pp. 338-357. [ crossref ]
- 2. Andersen, T., Chung, H. and Sorensen, B. (1999) Efficient method of moments estimation of a stochastic volatility model: a Monte Carlo study. Journal of Econometrics 91 , pp. 61-87. [ crossref ]
- 3. Asai, M. and McAleer, M. (2004) — Unpublished paper, Faculty of Economics, Tokyo Metropolitan University
- 4. Asai, M. and McAleer, M. (2005a) Dynamic asymmetric leverage in stochastic volatility models. Econometric Reviews 24 , pp. 317-332. [informaworld]
- 5. Asai, M. and McAleer, M. (2005b) Asymmetric multivariate stochastic volatility. Econometric Reviews 25:2-3 , pp. 453-473. [informaworld]
- 6. Asai, M. and McAleer, M. (2006) Finance Letters — To appear in
- 7. Bauwens, L., Laurent, S. and Rombouts, J. V. K. (2006) Multivariate GARCH: a survey. Journal of Applied Econometrics 21 , pp. 79-109. [ crossref ]
- 8. Bellman, R. (1970) Introduction to Matrix Analysis McGraw-Hill , New York
- 9. Berg, A., Meyer, R. and Yu, J. (2004) Deviance information criterion for comparing stochastic volatility models. Journal of Business and Economic Statistics 22 , pp. 107-120. [ crossref ]
- 10. Black, F. (1976) Studies of stock market volatility changes. pp. 177-181. — Proceedings of the American Statistical Association, Business and Economic Statistics Section
- 11. Bollerslev, T. (1990) Modelling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH approach. Review of Economics and Statistics 72 , pp. 498-505. [ crossref ]
- 12. Bos, C. S. and Shephard, N. (2006) Inference for adaptive time series models: stochastic volatility and conditionally gaussian state space form. Econometric Reviews 25:2-3 , pp. 219-244. [informaworld]
- 13. Broto, C. and Ruiz, E. (2004) Estimation methods for stochastic volatility models: a survey. Journal of Economic Surveys 18 , pp. 613-649.
- 14. Campbell, J. Y. and Hentschel, L. (1992) No news is good news: an asymmetric model of changing volatility in stock returns. Journal of Financial Economics 31 , pp. 281-318. [ crossref ]
- 15. Chan, D., Kohn, R. and Kirby, C. (2005) Multivariate stochastic volatility models with correlated errors. Econometric Reviews 25:2-3 , pp. 245-274. [informaworld]
- 16. Chesney, M. and Scott, L. O. (1989) Pricing European currency options: a comparison of the modified black-scholes model and a random variance model. Journal of Financial and Quantitative Analysis 24 , pp. 267-284. [ crossref ]
- 17. Chib, S. (1995) Marginal likelihood from the Gibbs output. Journal of the American Statistical Association 90 , pp. 1313-1321. [ crossref ]
- 18. Chib, S. Heckman, J. J. and Leamer, E. (eds) (2001) Handbook of Econometrics 5 , pp. 3569-3649. North-Holland
- 19. Chib, S., Nardari, F. and Shephard, N. (2005) Analysis of high dimensional multivariate stochastic volatility models. Journal of Econometrics — To appear in
- 20. Chiu, T. Y. M., Leonard, T. and Tsui, K.-W. (1996) The matrix-logarithmic covariance model. Journal of the American Statistical Association 91 , pp. 198-210. [ crossref ]
- 21. Christie, A. A. (1982) The stochastic behavior of common stock variances: value, leverage and interest rate effects. Journal of Financial Economics 10 , pp. 407-432. [ crossref ]
- 22. Christodoulakis, G. and Satchell, S. E. (2002) Correlated ARCH (CorrARCH): modelling the time-varying conditional correlation between financial asset returns. European Journal of Operational Research 139 , pp. 351-370. [ crossref ]
- 23. Cox, J., Ingersoll, J. and Ross, S. (1985) A theory of the term structure of interest rates. Econometrica 53 , pp. 385-407. [ crossref ]
- 24. Danielsson, J. (1994) Stochastic volatility in asset prices: estimation with simulated maximum likelihood. Journal of Econometrics 64 , pp. 375-400. [ crossref ]
- 25. Danielsson, J. (1998) Multivariate stochastic volatility models: estimation and a comparison with VGARCH models. Journal of Empirical Finance 5 , pp. 155-173. [ crossref ]
- 26. Danielsson, J. and Richard, J.-F. (1993) Quadratic acceleration for simulated maximum likelihood evaluation. Journal of Applied Econometrics 8 , pp. 153-173.
- 27. Diebold, F. X. and Nerlove, M. (1989) The dynamics of exchange rate volatility: a multivariate latent-factor ARCH model. Journal of Applied Econometrics 4 , pp. 1-22.
- 28. Ding, Z. and Engle, R. (2001) Large scale conditional covariance modelling, estimation and testing. Academia Economic Papers 29 , pp. 157-184.
- 29. Doz, C. and Renault, E. (2006) Factor stochastic volatility in mean models: a GMM approach. Econometric Reviews 25:2-3 , pp. 275-309. [informaworld]
- 30. Dunsmuir, W. (1979) A central limit theorem for parameter estimation in stationary vector time series and its application to models for a signal observed with noise. Annals of Statistics 7 , pp. 490-506.
- 31. Durbin, J. and Koopman, S. J. (1997) Monte Carlo maximum likelihood estimation for non-gaussian state space models. Biometrika 84 , pp. 669-684.
- 32. Durham, G. (2005) Monte Carlo methods for estimating, smoothing, filtering one- and two-factor stochastic volatility models. Journal of Econometrics — To appear in [ crossref ]
- 33. Engle, R. F. (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation. Econometrica 50 , pp. 987-1007. [ crossref ]
- 34. Engle, R. F. (2002) Dynamic conditional correlation: a simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business and Economic Statistics 20 , pp. 339-350. [ crossref ]
- 35. Engle, R. F. and Ng, V. (1993) Measuring and testing the impact of news in volatility. Journal of Finance 43 , pp. 1749-1778. [ crossref ]
- 36. Engle, R. F. and Kroner, K. F. (1995) Multivariate simultaneous generalized ARCH. Econometric Theory 11 , pp. 122-150.
- 37. Engle, R. F., Ng, V. and Rothschild, M. (1990) Asset pricing with a factor-ARCH covariance structure. Journal of Econometrics 45 , pp. 213-237. [ crossref ]
- 38. Gallant, A. R. and Tauchen, G. E. (1998) Reprojecting partially observed systems with application to interest rate diffusions. Journal of the American Statistical Association 93 , pp. 10-24. [ crossref ]
- 39. Geweke, J. and Porter-Hudak, S. (1983) The estimation and application of long memory time series models. Journal of Time Series Analysis 4 , pp. 221-238.
- 40. Ghysels, E., Harvey, A. C. and Renault, E. Rao, C. R. and Maddala, G. S. (eds) (1996) Statistical Models in Finance pp. 119-191. North-Holland , Amsterdam
- 41. Glosten, L., Jagannathan, R. and Runkle, D. (1993) On the relation between the expected value and volatility of nominal excess returns on stocks. Journal of Finance 46 , pp. 1779-1801. [ crossref ]
- 42. Gourieroux, C. (2006) Continuous time wishart process for stochastic risk. Econometric Reviews 25:2-3 , pp. 177-217. [informaworld]
- 43. Gourieroux, C., Jasiak, J. and Sufana, R. (2004) The wishart autoregressive process of multivariate stochastic volatility. — Unpublished paper, CREST and CEPREMAP, France
- 44. Han, Y. (2006) The economics value of volatility modelling: asset allocation with a high dimensional dynamic latent factor multivariate stochastic volatility model. Review of Financial Studies 19 , pp. 237-271. [ crossref ]
- 45. Harvey, A. C. and Shephard, N. (1996) Estimation of an asymmetric stochastic volatility model for asset returns. Journal of Business and Economic Statistics 14 , pp. 429-434. [ crossref ]
- 46. Harvey, A. C., Ruiz, E. and Shephard, N. (1994) Multivariate stochastic variance models. Review of Economic Studies 61 , pp. 247-264. [ crossref ]
- 47. Hull, J. and White, A. (1987) The pricing of options on assets with stochastic volatility. Journal of Finance 42 , pp. 281-300. [ crossref ]
- 48. Jacquier, E., Polson, N. G. and Rossi, P. E. (1994) Bayesian analysis of stochastic volatility models (with discussion). Journal of Business and Economic Statistics 12 , pp. 371-389. [ crossref ]
- 49. Jacquier, E., Polson, N. G. and Rossi, P. E. (1995) Models and priors for multivariate stochastic volatility. — CIRANO Working Paper No. 95s-18, Montreal
- 50. Jacquier, E., Polson, N. G. and Rossi, P. E. (1999) Stochastic volatility: univariate and multivariate extensions. — CIRANO Working paper 99s-26, Montreal
- 51. Jacquier, E., Polson, N. G. and Rossi, P. E. (2004) Bayesian analysis of stochastic volatility models with fat-tails and correlated errors. Journal of Econometrics 122 , pp. 185-212. [ crossref ]
- 52. Jungbacker, B. and Koopman, S. J. (2006) Monte Carlo likelihood estimation for three multivariate stochastic volatility models. Econometric Reviews 25:2-3 , pp. 385-408. [informaworld]
- 53. Kawakatsu, H. (2005) Matrix exponential GARCH. Journal of Econometrics — To appear in
- 54. Kim, S., Shephard, N. and Chib, S. (1998) Stochastic volatility: likelihood inference and comparison with ARCH models. Review of Economic Studies 65 , pp. 361-393.
- 55. Kitagawa, G. (1987) Non-Gaussian state-space modelling of non-stationary time series (with discussion). Journal of American Statistical Association 82 , pp. 1032-1063. [ crossref ]
- 56. Koopman, S. J. and Shephard, N. (2004) Estimating the likelihood of the stochastic volatility model: testing the assumption behind importance sampling. — Working paper, Nuffield College
- 57. Liesenfeld, R. and Richard, J.-F. (2003) Univariate and multivariate stochastic volatility models: estimation and diagnostics. Journal of Empirical Finance 10 , pp. 505-531. [ crossref ]
- 58. Liesenfeld, R. and Richard, J.-F. (2006) Classical and bayesian analysis of univariate and multivariate stochastic volatility models. Econometric Reviews 25:2-3 , pp. 335-360. [informaworld]
- 59. McAleer, M. (2005) Automated inference and learning in modeling financial volatility. Econometric Theory 21 , pp. 232-261. [ crossref ]
- 60. Meyer, R. and Yu, J. (2000) BUGS for a bayesian analysis of stochastic volatility models. Econometrics Journal 3 , pp. 198-215.
- 61. Nardari, F. and Scruggs, J. (2003) Analysis of linear factor models with multivariate stochastic volatility for stock and bond returns. — Unpublished paper, Department of Finance, Arizona State University
- 62. Nelson, D. B. (1991) Conditional heteroscedasticity in asset returns: a new approach. Econometrica 59 , pp. 347-370. [ crossref ]
- 63. Philipov, A. and Glickman, M. E. (2004) Multivariate stochastic volatility via Wishart processes. Journal of Business and Economic Statistics — To appear in
- 64. Philipov, A. and Glickman, M. E. (2006) Factor multivariate stochastic volatility via Wishart processes. Econometric Reviews 25:2-3 , pp. 311-334. [informaworld]
- 65. Pitt, M. and Shephard, N. Bernardo, J. M., Berger, J. O., David, A. P. and Smith, A. F. M. (eds) (1999a) Bayesian Statistics 6 pp. 547-570. Oxford University Press
- 66. Pitt, M. and Shephard, N. (1999b) Filtering via simulation: auxiliary particle filter. Journal of the American Statistical Association 94 , pp. 590-599. [ crossref ]
- 67. Quintana, J. M. and West, M. (1987) An analysis of international exchange rates using multivariate DLMs. The Statistician 36 , pp. 275-281. [ crossref ]
- 68. Ray, B. K. and Tsay, R. S. (2000) Long-range dependence in daily stock volatilities. Journal of Business and Economic Statistics 18 , pp. 254-262. [ crossref ]
- 69. Robinson, P. M. (1995) Log-periodogram regression with time series with long-range dependence. Annals of Statistics 23 , pp. 1048-1072.
- 70. Ross, S. A. (1976) The arbitrage theory of asset pricing. Journal of Economic Theory 13 , pp. 641-660. [ crossref ]
- 71. Sandmann, G. and Koopman, S. J. (1998) Estimation of stochastic volatility models via Monte Carlo maximum likelihood. Journal of Econometrics 87 , pp. 271-301. [ crossref ]
- 72. Shephard, N. Cox, D. R., Hinkley, D. V. and Barndorff-Nielsen, O. E. (eds) (1996) Time Series Models in Econometrics, Finance and Other Fields pp. 1-67. Chapman & Hall , London
- 73. Shephard, N. (2005) Stochastic Volatility: Selected Readings Oxford University Press , Oxford
- 74. Shephard, N. and Pitt, M. K. (1997) Likelihood analysis of non-gaussian measurement time series. Biometrika 84 , pp. 653-667.
- 75. Smith, M. and Pitts, A. (2006) Foreign exchange intervention by the bank of Japan: Bayesian analysis using a bivariate stochastic volatility model. Econometric Reviews 25:2-3 , pp. 425-451. [informaworld]
- 76. So, M. K. P., Li, W. K. and Lam, K. (2002) A threshold stochastic volatility model. Journal of Forecasting 21 , pp. 473-500. [ crossref ]
- 77. Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and van der Linde, A. (2002) Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statistical Society, Series B 64 , pp. 583-639. [ crossref ]
- 78. Taylor, S. J. Anderson, O. D. (ed) (1982) Time Series Analysis: Theory and Practice 1 , pp. 203-226. North-Holland
- 79. Taylor, S. J. (1986) Modelling Financial Time Series John Wiley , Chichester
- 80. Tierney, L. (1994) Markov chains for exploring posterior distributions. Annals of Statistics 22 , pp. 1701-1762.
- 81. Tims, B. and Mahieu, R. (2003) A range-based multivariate stochastic volatility model for exchange rates. Econometric Reviews 25:2-3 , pp. 409-424. [informaworld]
- 82. Tsay, R. S. (2002) Analysis of Financial Time Series: Financial Econometrics John Wiley , New York [ crossref ]
- 83. Tse, Y. K. and Tsui, A. K. C. (2002) A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlations. Journal of Business and Economic Statistics 20 , pp. 351-362. [ crossref ]
- 84. Wiggins, J. B. (1987) Option values under stochastic volatility: theory and empirical estimates. Journal of Financial Economics 19 , pp. 351-372. [ crossref ]
- 85. Yu, J. (2005) On leverage in a stochastic volatility model. Journal of Econometrics 127 , pp. 165-178. [ crossref ]
- 86. Yu, J. and Meyer, R. (2006) Multivariate stochastic volatility models: Bayesian estimation and model comparison. Econometric Reviews 25:2-3 , pp. 361-384. [informaworld]

Download Citation