Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1608.08468.html
   My bibliography  Save this paper

Sparse Bayesian time-varying covariance estimation in many dimensions

Author

Listed:
  • Gregor Kastner
Abstract
We address the curse of dimensionality in dynamic covariance estimation by modeling the underlying co-volatility dynamics of a time series vector through latent time-varying stochastic factors. The use of a global-local shrinkage prior for the elements of the factor loadings matrix pulls loadings on superfluous factors towards zero. To demonstrate the merits of the proposed framework, the model is applied to simulated data as well as to daily log-returns of 300 S&P 500 members. Our approach yields precise correlation estimates, strong implied minimum variance portfolio performance and superior forecasting accuracy in terms of log predictive scores when compared to typical benchmarks.

Suggested Citation

  • Gregor Kastner, 2016. "Sparse Bayesian time-varying covariance estimation in many dimensions," Papers 1608.08468, arXiv.org, revised Nov 2017.
    • Handle: RePEc:arx:papers:1608.08468
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1608.08468
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Roman Liesenfeld & Jean-Francois Richard, 2006. "Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 335-360.
    2. Korobilis, Dimitris, 2013. "Hierarchical shrinkage priors for dynamic regressions with many predictors," International Journal of Forecasting, Elsevier, vol. 29(1), pages 43-59.
    3. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    4. 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.
    5. Villani, Mattias & Kohn, Robert & Giordani, Paolo, 2009. "Regression density estimation using smooth adaptive Gaussian mixtures," Journal of Econometrics, Elsevier, vol. 153(2), pages 155-173, December.
    6. Zhou, Xiaocong & Nakajima, Jouchi & West, Mike, 2014. "Bayesian forecasting and portfolio decisions using dynamic dependent sparse factor models," International Journal of Forecasting, Elsevier, vol. 30(4), pages 963-980.
    7. Geweke, John & Amisano, Gianni, 2010. "Comparing and evaluating Bayesian predictive distributions of asset returns," International Journal of Forecasting, Elsevier, vol. 26(2), pages 216-230, April.
    8. repec:taf:jnlbes:v:30:y:2012:i:2:p:212-228 is not listed on IDEAS
    9. Huber, Florian, 2016. "Density forecasting using Bayesian global vector autoregressions with stochastic volatility," International Journal of Forecasting, Elsevier, vol. 32(3), pages 818-837.
    10. 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.
    11. Miguel A.G. Belmonte & Gary Koop & Dimitris Korobilis, 2014. "Hierarchical Shrinkage in Time‐Varying Parameter Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(1), pages 80-94, January.
    12. Florian Huber & Gregor Kastner & Martin Feldkircher, 2016. "Should I stay or should I go? A latent threshold approach to large-scale mixture innovation models," Papers 1607.04532, arXiv.org, revised Jul 2018.
    13. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
    14. Cavit Pakel & Neil Shephard & Kevin Sheppard & Robert F. Engle, 2021. "Fitting Vast Dimensional Time-Varying Covariance Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(3), pages 652-668, July.
    15. repec:ulb:ulbeco:2013/13388 is not listed on IDEAS
    16. Marta Banbura & Domenico Giannone & Lucrezia Reichlin, 2010. "Large Bayesian vector auto regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(1), pages 71-92.
    17. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    18. Sentana, Enrique & Fiorentini, Gabriele, 2001. "Identification, estimation and testing of conditionally heteroskedastic factor models," Journal of Econometrics, Elsevier, vol. 102(2), pages 143-164, June.
    19. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2016. "Common Drifting Volatility in Large Bayesian VARs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 375-390, July.
    20. Florian Huber & Martin Feldkircher, 2019. "Adaptive Shrinkage in Bayesian Vector Autoregressive Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(1), pages 27-39, January.
    21. Yufeng Han, 2006. "Asset Allocation with a High Dimensional Latent Factor Stochastic Volatility Model," The Review of Financial Studies, Society for Financial Studies, vol. 19(1), pages 237-271.
    22. Koop, Gary & Korobilis, Dimitris, 2013. "Large time-varying parameter VARs," Journal of Econometrics, Elsevier, vol. 177(2), pages 185-198.
    23. A. Bhattacharya & D. B. Dunson, 2011. "Sparse Bayesian infinite factor models," Biometrika, Biometrika Trust, vol. 98(2), pages 291-306.
    24. Kastner, Gregor, 2016. "Dealing with Stochastic Volatility in Time Series Using the R Package stochvol," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(i05).
    25. Tsunehiro Ishihara & Yasuhiro Omori, 2017. "Portfolio optimization using dynamic factor and stochastic volatility: evidence on Fat-tailed errors and leverage," The Japanese Economic Review, Japanese Economic Association, vol. 68(1), pages 63-94, March.
    26. 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.
    27. Malin Adolfson & Jesper Linde & Mattias Villani, 2007. "Forecasting Performance of an Open Economy DSGE Model," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 289-328.
    28. Dong Hwan Oh & Andrew J. Patton, 2017. "Modeling Dependence in High Dimensions With Factor Copulas," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 139-154, January.
    29. Baştürk, N. & Borowska, A. & Grassi, S. & Hoogerheide, L. & van Dijk, H.K., 2019. "Forecast density combinations of dynamic models and data driven portfolio strategies," Journal of Econometrics, Elsevier, vol. 210(1), pages 170-186.
    30. Frühwirth-Schnatter, Sylvia & Wagner, Helga, 2010. "Stochastic model specification search for Gaussian and partial non-Gaussian state space models," Journal of Econometrics, Elsevier, vol. 154(1), pages 85-100, January.
    31. Marta Banbura & Domenico Giannone & Lucrezia Reichlin, 2010. "Large Bayesian vector auto regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(1), pages 71-92.
    32. 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.
    33. Roman Liesenfeld & Robert C. Jung, 2000. "Stochastic volatility models: conditional normality versus heavy-tailed distributions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(2), pages 137-160.
    34. Borus Jungbacker & Siem Jan Koopman, 2006. "Monte Carlo Likelihood Estimation for Three Multivariate Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 385-408.
    35. Daniel Felix Ahelegbey & Monica Billio & Roberto Casarin, 2016. "Bayesian Graphical Models for STructural Vector Autoregressive Processes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(2), pages 357-386, March.
    36. Zoey Yi Zhao & Meng Xie & Mike West, 2016. "Dynamic dependence networks: Financial time series forecasting and portfolio decisions," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 32(3), pages 311-332, May.
    37. Carhart, Mark M, 1997. "On Persistence in Mutual Fund Performance," Journal of Finance, American Finance Association, vol. 52(1), pages 57-82, March.
    38. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 247-264.
    39. Tsunehiro Ishihara & Yasuhiro Omori, 2017. "Portfolio optimization using dynamic factor and stochastic volatility: evidence on Fat-tailed errors and leverage," The Japanese Economic Review, Springer, vol. 68(1), pages 63-94, March.
    40. Gregor Kastner & Florian Huber, 2020. "Sparse Bayesian vector autoregressions in huge dimensions," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(7), pages 1142-1165, November.
    41. Nalan Basturk & Stefano Grassi & Lennart Hoogerheide & Herman K. van Dijk, 2016. "Time-varying Combinations of Bayesian Dynamic Models and Equity Momentum Strategies," Tinbergen Institute Discussion Papers 16-099/III, Tinbergen Institute.
    42. Zoey Zhao & Meng Xie & Mike West, 2016. "Rejoinder to ‘Dynamic dependence networks: Financial time series forecasting and portfolio decisions’," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 32(3), pages 336-339, May.
    43. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    44. Philipov, Alexander & Glickman, Mark E., 2006. "Multivariate Stochastic Volatility via Wishart Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 313-328, July.
    45. Alexander Philipov & Mark Glickman, 2006. "Factor Multivariate Stochastic Volatility via Wishart Processes," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 311-334.
    46. Florian Huber & Gregor Kastner & Martin Feldkircher, 2019. "Should I stay or should I go? A latent threshold approach to large‐scale mixture innovation models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(5), pages 621-640, August.
    47. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
    48. Sylvia Kaufmann & Christian Schumacher, 2013. "Bayesian estimation of sparse dynamic factor models with order-independent identification," Working Papers 13.04, Swiss National Bank, Study Center Gerzensee.
    49. 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. 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.
    2. Hauzenberger, Niko, 2021. "Flexible Mixture Priors for Large Time-varying Parameter Models," Econometrics and Statistics, Elsevier, vol. 20(C), pages 87-108.
    3. Gregor Kastner & Florian Huber, 2020. "Sparse Bayesian vector autoregressions in huge dimensions," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(7), pages 1142-1165, November.
    4. Niko Hauzenberger, 2020. "Flexible Mixture Priors for Large Time-varying Parameter Models," Papers 2006.10088, arXiv.org, revised Nov 2020.
    5. 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.
    6. Lopes, Hedibert F. & McCulloch, Robert E. & Tsay, Ruey S., 2022. "Parsimony inducing priors for large scale state–space models," Journal of Econometrics, Elsevier, vol. 230(1), pages 39-61.
    7. 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.
    8. Michael Pfarrhofer, 2024. "Forecasts with Bayesian vector autoregressions under real time conditions," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(3), pages 771-801, April.
    9. McCausland, William & Miller, Shirley & Pelletier, Denis, 2021. "Multivariate stochastic volatility using the HESSIAN method," Econometrics and Statistics, Elsevier, vol. 17(C), pages 76-94.
    10. Joshua Chan, 2023. "BVARs and Stochastic Volatility," Papers 2310.14438, arXiv.org.
    11. 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.
    12. Anthony N. Rezitis & Gregor Kastner, 2021. "On the joint volatility dynamics in dairy markets," Papers 2104.12707, arXiv.org.
    13. Bitto, Angela & Frühwirth-Schnatter, Sylvia, 2019. "Achieving shrinkage in a time-varying parameter model framework," Journal of Econometrics, Elsevier, vol. 210(1), pages 75-97.
    14. Pfarrhofer, Michael, 2023. "Measuring International Uncertainty Using Global Vector Autoregressions with Drifting Parameters," Macroeconomic Dynamics, Cambridge University Press, vol. 27(3), pages 770-793, April.
    15. Chan, Joshua C.C., 2023. "Comparing stochastic volatility specifications for large Bayesian VARs," Journal of Econometrics, Elsevier, vol. 235(2), pages 1419-1446.
    16. Tsionas, Mike G. & Izzeldin, Marwan & Trapani, Lorenzo, 2022. "Estimation of large dimensional time varying VARs using copulas," European Economic Review, Elsevier, vol. 141(C).
    17. Mike K. P. So & C. Y. Choi, 2009. "A threshold factor multivariate stochastic volatility model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(8), pages 712-735.
    18. Todd E. Clark & Florian Huber & Gary Koop & Massimiliano Marcellino & Michael Pfarrhofer, 2023. "Tail Forecasting With Multivariate Bayesian Additive Regression Trees," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(3), pages 979-1022, August.
    19. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    20. Dovern, Jonas & Feldkircher, Martin & Huber, Florian, 2016. "Does joint modelling of the world economy pay off? Evaluating global forecasts from a Bayesian GVAR," Journal of Economic Dynamics and Control, Elsevier, vol. 70(C), pages 86-100.

    More about this item

    JEL classification:

    • 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
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:1608.08468. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.