IDEAS home Printed from https://ideas.repec.org/a/gam/jecnmx/v12y2024i1p5-d1341433.html
   My bibliography  Save this article

Multivariate Stochastic Volatility Modeling via Integrated Nested Laplace Approximations: A Multifactor Extension

Author

Listed:
  • João Pedro Coli de Souza Monteneri Nacinben

    (Department of Economics, FEARP-University of São Paulo, Ribeirão Preto 14040-905, Brazil
    These authors contributed equally to this work.)

  • Márcio Laurini

    (Department of Economics, FEARP-University of São Paulo, Ribeirão Preto 14040-905, Brazil
    These authors contributed equally to this work.)

Abstract

This study introduces a multivariate extension to the class of stochastic volatility models, employing integrated nested Laplace approximations (INLA) for estimation. Bayesian methods for estimating stochastic volatility models through Markov Chain Monte Carlo (MCMC) can become computationally burdensome or inefficient as the dataset size and problem complexity increase. Furthermore, issues related to chain convergence can also arise. In light of these challenges, this research aims to establish a computationally efficient approach for estimating multivariate stochastic volatility models. We propose a multifactor formulation estimated using the INLA methodology, enabling an approach that leverages sparse linear algebra and parallelization techniques. To evaluate the effectiveness of our proposed model, we conduct in-sample and out-of-sample empirical analyses of stock market index return series. Furthermore, we provide a comparative analysis with models estimated using MCMC, demonstrating the computational efficiency and goodness of fit improvements achieved with our approach.

Suggested Citation

  • João Pedro Coli de Souza Monteneri Nacinben & Márcio Laurini, 2024. "Multivariate Stochastic Volatility Modeling via Integrated Nested Laplace Approximations: A Multifactor Extension," Econometrics, MDPI, vol. 12(1), pages 1-28, February.
  • Handle: RePEc:gam:jecnmx:v:12:y:2024:i:1:p:5-:d:1341433
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2225-1146/12/1/5/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2225-1146/12/1/5/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kastner, Gregor & Frühwirth-Schnatter, Sylvia, 2014. "Ancillarity-sufficiency interweaving strategy (ASIS) for boosting MCMC estimation of stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 408-423.
    2. Gunawan, David & Kohn, Robert & Nott, David, 2021. "Variational Bayes approximation of factor stochastic volatility models," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1355-1375.
    3. Van Niekerk, Janet & Krainski, Elias & Rustand, Denis & Rue, Håvard, 2023. "A new avenue for Bayesian inference with INLA," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    4. Harvey, Andrew C & Shephard, Neil, 1996. "Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 429-434, October.
    5. Sara Martino & Kjersti Aas & Ola Lindqvist & Linda Neef & Håvard Rue, 2011. "Estimating stochastic volatility models using integrated nested Laplace approximations," The European Journal of Finance, Taylor & Francis Journals, vol. 17(7), pages 487-503.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. Sylvia Frühwirth-Schnatter & Darjus Hosszejni & Hedibert Freitas Lopes, 2023. "When It Counts—Econometric Identification of the Basic Factor Model Based on GLT Structures," Econometrics, MDPI, vol. 11(4), pages 1-30, November.
    8. 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.
    9. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Linde, 2014. "The deviance information criterion: 12 years on," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(3), pages 485-493, June.
    10. Jorge Alberto Achcar & Edilberto Cepeda-Cuervo & Milton Barossi-Filho, 2012. "Multivariate volatility models: an application to IBOVESPA and Dow Jones Industrial," Revista Cuadernos de Economia, Universidad Nacional de Colombia, FCE, CID, June.
    11. Sandmann, Gleb & Koopman, Siem Jan, 1998. "Estimation of stochastic volatility models via Monte Carlo maximum likelihood," Journal of Econometrics, Elsevier, vol. 87(2), pages 271-301, September.
    12. Gregor Kastner & Sylvia Fruhwirth-Schnatter & Hedibert Freitas Lopes, 2016. "Efficient Bayesian Inference for Multivariate Factor Stochastic Volatility Models," Papers 1602.08154, arXiv.org, revised Jul 2017.
    Full references (including those not matched with items on IDEAS)

    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. M. Hakan Eratalay, 2016. "Estimation of Multivariate Stochastic Volatility Models: A Comparative Monte Carlo Study," International Econometric Review (IER), Econometric Research Association, vol. 8(2), pages 19-52, September.
    2. Paolo Girardello & Orietta Nicolis & Giovanni Tondini, 2003. "Comparing Conditional Variance Models: Theory and Empirical Evidence," Multinational Finance Journal, Multinational Finance Journal, vol. 7(3-4), pages 177-206, September.
    3. P. Girardello & Orietta Nicolis & Giovanni Tondini, 2002. "Comparing conditional variance models: Theory and empirical evidence," Departmental Working Papers 2002-08, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    4. Shang, Yuhuang & Zheng, Tingguo, 2021. "Mixed-frequency SV model for stock volatility and macroeconomics," Economic Modelling, Elsevier, vol. 95(C), pages 462-472.
    5. Antonis Demos, 2023. "Estimation of Asymmetric Stochastic Volatility in Mean Models," DEOS Working Papers 2309, Athens University of Economics and Business.
    6. Siem Jan Koopman & Eugenie Hol Uspensky, 2002. "The stochastic volatility in mean model: empirical evidence from international stock markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(6), pages 667-689.
    7. Amir Atiya & Steve Wall, 2009. "An analytic approximation of the likelihood function for the Heston model volatility estimation problem," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 289-296.
    8. Rezitis, Anthony N. & Kastner, Gregor, 2021. "On the joint volatility dynamics in international dairy commodity markets," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 60(2), January.
    9. Sakaria, D.K. & Griffin, J.E., 2017. "On efficient Bayesian inference for models with stochastic volatility," Econometrics and Statistics, Elsevier, vol. 3(C), pages 23-33.
    10. Breitung, Jörg & Hafner, Christian M., 2016. "A simple model for now-casting volatility series," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1247-1255.
    11. M. Angeles Carnero, 2004. "Persistence and Kurtosis in GARCH and Stochastic Volatility Models," Journal of Financial Econometrics, Oxford University Press, vol. 2(2), pages 319-342.
    12. Anthony N. Rezitis & Gregor Kastner, 2021. "On the joint volatility dynamics in dairy markets," Papers 2104.12707, arXiv.org.
    13. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," LIDAM Discussion Papers CORE 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
      • Bauwens, L. & Hafner C. & Laurent, S., 2011. "Volatility Models," LIDAM Discussion Papers ISBA 2011044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
      • Bauwens, L. & Hafner, C. & Laurent, S., 2012. "Volatility Models," LIDAM Reprints ISBA 2012028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. Philipp Otto & Osman Dou{g}an & Suleyman Tac{s}p{i}nar & Wolfgang Schmid & Anil K. Bera, 2023. "Spatial and Spatiotemporal Volatility Models: A Review," Papers 2308.13061, arXiv.org.
    15. 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.
    16. M. Hakan Eratalay, 2016. "Estimation of Multivariate Stochastic Volatility Models: A Comparative Monte Carlo Study," International Econometric Review (IER), Econometric Research Association, vol. 8(2), pages 19-52, September.
    17. Smith Daniel R, 2009. "Asymmetry in Stochastic Volatility Models: Threshold or Correlation?," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(3), pages 1-36, May.
    18. Alexander Tsyplakov, 2010. "Revealing the arcane: an introduction to the art of stochastic volatility models (in Russian)," Quantile, Quantile, issue 8, pages 69-122, July.
    19. Cross, Jamie L. & Hou, Chenghan & Trinh, Kelly, 2021. "Returns, volatility and the cryptocurrency bubble of 2017–18," Economic Modelling, Elsevier, vol. 104(C).
    20. Bermudez, P. de Zea & Marín, J. Miguel & Rue, Håvard & Veiga, Helena, 2024. "Integrated nested Laplace approximations for threshold stochastic volatility models," Econometrics and Statistics, Elsevier, vol. 30(C), pages 15-35.

    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:gam:jecnmx:v:12:y:2024:i:1:p:5-:d:1341433. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.