IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v43y2022i1p147-153.html
   My bibliography  Save this article

On the Relationship between Uhlig Extended and beta‐Bartlett Processes

Author

Listed:
  • Víctor Peña
  • Kaoru Irie

Abstract

Stochastic volatility processes are used in multi‐variate time series analysis to track time‐varying patterns in covariance matrices. Uhlig extended (UE) and beta‐Bartlett (BB) processes are especially convenient for analyzing high‐dimensional time series because they are conjugate with Wishart likelihoods. In this article, we show that UE and BB are closely related, but not equivalent: their hyperparameters can be matched so that they have the same forward‐filtered posteriors and one‐step ahead forecasts, but different joint (smoothed) posterior distributions. Under this circumstance, Bayes factors cannot discriminate the models and alternative approaches to model comparison are needed. We illustrate these issues in a retrospective analysis of volatilities of returns of foreign exchange rates. Additionally, we provide a backward sampling algorithm for the BB process, for which retrospective analysis had not been developed.

Suggested Citation

  • Víctor Peña & Kaoru Irie, 2022. "On the Relationship between Uhlig Extended and beta‐Bartlett Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(1), pages 147-153, January.
    • Handle: RePEc:bla:jtsera:v:43:y:2022:i:1:p:147-153
    DOI: 10.1111/jtsa.12595
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/jtsa.12595
    Download Restriction: no
    File URL: https://libkey.io/10.1111/jtsa.12595?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Jouchi Nakajima & Mike West, 2012. "Dynamic Factor Volatility Modeling: A Bayesian Latent Threshold Approach," Journal of Financial Econometrics, Oxford University Press, vol. 11(1), pages 116-153, December.
    2. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    3. 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.
    4. Harald Uhlig, 1997. "Bayesian Vector Autoregressions with Stochastic Volatility," Econometrica, Econometric Society, vol. 65(1), pages 59-74, January.
    5. Gelman Andrew & Robert Christian P. & Rousseau Judith, 2013. "Inherent difficulties of non-Bayesian likelihood-based inference, as revealed by an examination of a recent book by Aitkin," Statistics & Risk Modeling, De Gruyter, vol. 30(2), pages 105-120, June.
    6. Mike West, 2020. "Bayesian forecasting of multivariate time series: scalability, structure uncertainty and decisions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 1-31, February.
    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. K. Triantafyllopoulos, 2012. "Multi‐variate stochastic volatility modelling using Wishart autoregressive processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(1), pages 48-60, January.
    2. João F. Caldeira & Guilherme V. Moura & Francisco J. Nogales & André A. P. Santos, 2017. "Combining Multivariate Volatility Forecasts: An Economic-Based Approach," Journal of Financial Econometrics, Oxford University Press, vol. 15(2), pages 247-285.
    3. K. Triantafyllopoulos, 2008. "Multivariate stochastic volatility using state space models," Papers 0802.0223, arXiv.org.
    4. K. Triantafyllopoulos, 2008. "Multivariate stochastic volatility with Bayesian dynamic linear models," Papers 0802.0214, arXiv.org.
    5. João Caldeira & Guilherme Moura & André A.P. Santos, 2012. "Portfolio optimization using a parsimonious multivariate GARCH model: application to the Brazilian stock market," Economics Bulletin, AccessEcon, vol. 32(3), pages 1848-1857.
    6. Santos, André A.P. & Nogales, Francisco J. & Ruiz, Esther & Dijk, Dick Van, 2012. "Optimal portfolios with minimum capital requirements," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 1928-1942.
    7. Carlos Trucíos & João H. G. Mazzeu & Marc Hallin & Luiz K. Hotta & Pedro L. Valls Pereira & Mauricio Zevallos, 2022. "Forecasting Conditional Covariance Matrices in High-Dimensional Time Series: A General Dynamic Factor Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(1), pages 40-52, December.
    8. Sentana, Enrique & Calzolari, Giorgio & Fiorentini, Gabriele, 2008. "Indirect estimation of large conditionally heteroskedastic factor models, with an application to the Dow 30 stocks," Journal of Econometrics, Elsevier, vol. 146(1), pages 10-25, September.
    9. 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.
    10. Yuta Kurose & Yasuhiro Omori, 2016. "Multiple-block Dynamic Equicorrelations with Realized Measures, Leverage and Endogeneity," CIRJE F-Series CIRJE-F-1022, CIRJE, Faculty of Economics, University of Tokyo.
    11. Joshua Chan, 2023. "BVARs and Stochastic Volatility," Papers 2310.14438, arXiv.org.
    12. Asai, Manabu & Caporin, Massimiliano & McAleer, Michael, 2015. "Forecasting Value-at-Risk using block structure multivariate stochastic volatility models," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 40-50.
    13. 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.
    14. Arias, Jonas E. & Rubio-Ramírez, Juan F. & Shin, Minchul, 2023. "Macroeconomic forecasting and variable ordering in multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1054-1086.
    15. Rodriguez, Abel & Puggioni, Gavino, 2010. "Mixed frequency models: Bayesian approaches to estimation and prediction," International Journal of Forecasting, Elsevier, vol. 26(2), pages 293-311, April.
    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. Caldeira, João F & Moura, Guilherme Valle & Santos, André Alves Portela, 2013. "Seleção de carteiras utilizando o modelo Fama-French-Carhart," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 67(1), April.
    18. Shirota, Shinichiro & Omori, Yasuhiro & F. Lopes, Hedibert. & Piao, Haixiang, 2017. "Cholesky realized stochastic volatility model," Econometrics and Statistics, Elsevier, vol. 3(C), pages 34-59.
    19. Soyer, Refik & Tanyeri, Kadir, 2006. "Bayesian portfolio selection with multi-variate random variance models," European Journal of Operational Research, Elsevier, vol. 171(3), pages 977-990, June.
    20. Jun Yu & Renate Meyer, 2006. "Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 361-384.

    More about this item

    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:bla:jtsera:v:43:y:2022:i:1:p:147-153. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.