IDEAS home Printed from https://ideas.repec.org/a/bes/jnlbes/v29i3y2011p342-355.html
   My bibliography  Save this article

Selection of Multivariate Stochastic Volatility Models via Bayesian Stochastic Search

Author

Listed:
  • Loddo, Antonello
  • Ni, Shawn
  • Sun, Dongchu

Abstract

We propose a Bayesian stochastic search approach to selecting restrictions on multivariate regression models where the errors exhibit deterministic or stochastic conditional volatilities. We develop a Markov chain Monte Carlo (MCMC) algorithm that generates posterior restrictions on the regression coefficients and Cholesky decompositions of the covariance matrix of the errors. Numerical simulations with artificially generated data show that the proposed method is effective in selecting the data-generating model restrictions and improving the forecasting performance of the model. Applying the method to daily foreign exchange rate data, we conduct stochastic search on a VAR model with stochastic conditional volatilities.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Loddo, Antonello & Ni, Shawn & Sun, Dongchu, 2011. "Selection of Multivariate Stochastic Volatility Models via Bayesian Stochastic Search," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(3), pages 342-355.
    • Handle: RePEc:bes:jnlbes:v:29:i:3:y:2011:p:342-355
    as

    Download full text from publisher

    File URL: http://pubs.amstat.org/doi/abs/10.1198/jbes.2010.08197
    File Function: full text
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    2. Alejandro Justiniano & Giorgio E. Primiceri, 2008. "The Time-Varying Volatility of Macroeconomic Fluctuations," American Economic Review, American Economic Association, vol. 98(3), pages 604-641, June.
    3. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    4. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-417, October.
    5. Inoue, Atsushi & Kilian, Lutz, 2008. "How Useful Is Bagging in Forecasting Economic Time Series? A Case Study of U.S. Consumer Price Inflation," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 511-522, June.
    6. Chun Liu & John M. Maheu, 2009. "Forecasting realized volatility: a Bayesian model-averaging approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(5), pages 709-733.
    7. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
    8. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2006. "Analysis of high dimensional multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 134(2), pages 341-371, October.
    9. Aguilar, Omar & West, Mike, 2000. "Bayesian Dynamic Factor Models and Portfolio Allocation," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 338-357, July.
    10. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    11. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    12. 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.
    13. Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 183-204, April.
    14. Harald Uhlig, 1997. "Bayesian Vector Autoregressions with Stochastic Volatility," Econometrica, Econometric Society, vol. 65(1), pages 59-74, January.
    15. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    16. Eugenie Hol & Siem Jan Koopman, 2002. "Stock Index Volatility Forecasting with High Frequency Data," Tinbergen Institute Discussion Papers 02-068/4, Tinbergen Institute.
    17. W. R. Gilks & P. Wild, 1992. "Adaptive Rejection Sampling for Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 337-348, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Manabu Asai & Chia-Lin Chang & Michael McAleer, 2016. "Realized Matrix-Exponential Stochastic Volatility with Asymmetry, Long Memory and Spillovers," Documentos de Trabajo del ICAE 2016-15, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    2. Roberto Casarin & Marco Tronzano & Domenico Sartore, 2013. "Bayesian Markov Switching Stochastic Correlation Models," Working Papers 2013:11, Department of Economics, University of Venice "Ca' Foscari".
    3. Kastner, Gregor, 2019. "Sparse Bayesian time-varying covariance estimation in many dimensions," Journal of Econometrics, Elsevier, vol. 210(1), pages 98-115.
    4. Ishihara, Tsunehiro & Omori, Yasuhiro & Asai, Manabu, 2016. "Matrix exponential stochastic volatility with cross leverage," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 331-350.
    5. Roberto Casarin & Domenico Sartore & Marco Tronzano, 2018. "A Bayesian Markov-Switching Correlation Model for Contagion Analysis on Exchange Rate Markets," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 101-114, January.
    6. Asai, Manabu & Chang, Chia-Lin & McAleer, Michael, 2022. "Realized matrix-exponential stochastic volatility with asymmetry, long memory and higher-moment spillovers," Journal of Econometrics, Elsevier, vol. 227(1), pages 285-304.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Willy Alanya & Gabriel Rodríguez, 2018. "Stochastic Volatility in the Peruvian Stock Market and Exchange Rate Returns: A Bayesian Approximation," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 17(3), pages 354-385, December.
    2. Font, Begoña, 1998. "Modelización de series temporales financieras. Una recopilación," DES - Documentos de Trabajo. Estadística y Econometría. DS 3664, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    4. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    5. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    6. Gael M. Martin & David T. Frazier & Ruben Loaiza-Maya & Florian Huber & Gary Koop & John Maheu & Didier Nibbering & Anastasios Panagiotelis, 2023. "Bayesian Forecasting in the 21st Century: A Modern Review," Monash Econometrics and Business Statistics Working Papers 1/23, Monash University, Department of Econometrics and Business Statistics.
    7. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Univariate and multivariate stochastic volatility models: estimation and diagnostics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 505-531, September.
    8. Martin, Gael M. & Frazier, David T. & Maneesoonthorn, Worapree & Loaiza-Maya, Rubén & Huber, Florian & Koop, Gary & Maheu, John & Nibbering, Didier & Panagiotelis, Anastasios, 2024. "Bayesian forecasting in economics and finance: A modern review," International Journal of Forecasting, Elsevier, vol. 40(2), pages 811-839.
    9. Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
    10. McCausland, William & Miller, Shirley & Pelletier, Denis, 2021. "Multivariate stochastic volatility using the HESSIAN method," Econometrics and Statistics, Elsevier, vol. 17(C), pages 76-94.
    11. Avouyi-Dovi, S. & Horny, G. & Sevestre, P., 2013. "The dynamics of bank loans short-term interest rates in the Euro area: what lessons can we draw from the current crisis?," Working papers 462, Banque de France.
    12. Du, Xiaodong & Yu, Cindy L. & Hayes, Dermot J., 2011. "Speculation and volatility spillover in the crude oil and agricultural commodity markets: A Bayesian analysis," Energy Economics, Elsevier, vol. 33(3), pages 497-503, May.
    13. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
    14. G. Dhaene, 2004. "Indirect Inference for Stochastic Volatility Models via the Log-Squared Observations," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business (FEB), Review of Business and Economic Literature, vol. 0(3), pages 421-440.
    15. Yu, Jun & Yang, Zhenlin & Zhang, Xibin, 2006. "A class of nonlinear stochastic volatility models and its implications for pricing currency options," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2218-2231, December.
    16. Charles Bos & Neil Shephard, 2006. "Inference for Adaptive Time Series Models: Stochastic Volatility and Conditionally Gaussian State Space Form," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 219-244.
    17. Legrand, Romain, 2018. "Time-Varying Vector Autoregressions: Efficient Estimation, Random Inertia and Random Mean," MPRA Paper 88925, University Library of Munich, Germany.
    18. Vo, Minh T., 2009. "Regime-switching stochastic volatility: Evidence from the crude oil market," Energy Economics, Elsevier, vol. 31(5), pages 779-788, September.
    19. Griffin, J.E. & Steel, M.F.J., 2006. "Inference with non-Gaussian Ornstein-Uhlenbeck processes for stochastic volatility," Journal of Econometrics, Elsevier, vol. 134(2), pages 605-644, October.
    20. Degiannakis, Stavros & Xekalaki, Evdokia, 2004. "Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review," MPRA Paper 80487, University Library of Munich, Germany.

    More about this item

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bes:jnlbes:v:29:i:3:y:2011:p:342-355. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Christopher F. Baum (email available below). General contact details of provider: http://www.amstat.org/publications/jbes/index.cfm?fuseaction=main .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.