IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2404.13986.html
   My bibliography  Save this paper

Stochastic Volatility in Mean: Efficient Analysis by a Generalized Mixture Sampler

Author

Listed:
  • Daichi Hiraki
  • Siddhartha Chib
  • Yasuhiro Omori

Abstract

In this paper we consider the simulation-based Bayesian analysis of stochastic volatility in mean (SVM) models. Extending the highly efficient Markov chain Monte Carlo mixture sampler for the SV model proposed in Kim et al. (1998) and Omori et al. (2007), we develop an accurate approximation of the non-central chi-squared distribution as a mixture of thirty normal distributions. Under this mixture representation, we sample the parameters and latent volatilities in one block. We also detail a correction of the small approximation error by using additional Metropolis-Hastings steps. The proposed method is extended to the SVM model with leverage. The methodology and models are applied to excess holding yields and S&P500 returns in empirical studies, and the SVM models are shown to outperform other volatility models based on marginal likelihoods.

Suggested Citation

  • Daichi Hiraki & Siddhartha Chib & Yasuhiro Omori, 2024. "Stochastic Volatility in Mean: Efficient Analysis by a Generalized Mixture Sampler," Papers 2404.13986, arXiv.org, revised Nov 2024.
  • Handle: RePEc:arx:papers:2404.13986
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2404.13986
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Berument, Hakan & Yalcin, Yeliz & Yildirim, Julide, 2009. "The effect of inflation uncertainty on inflation: Stochastic volatility in mean model within a dynamic framework," Economic Modelling, Elsevier, vol. 26(6), pages 1201-1207, November.
    2. 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.
    3. Haroon Mumtaz & Francesco Zanetti, 2013. "The Impact of the Volatility of Monetary Policy Shocks," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(4), pages 535-558, June.
    4. Joshua C. C. Chan, 2017. "The Stochastic Volatility in Mean Model With Time-Varying Parameters: An Application to Inflation Modeling," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 17-28, January.
    5. Cross, Jamie L. & Hou, Chenghan & Koop, Gary & Poon, Aubrey, 2023. "Large stochastic volatility in mean VARs," Journal of Econometrics, Elsevier, vol. 236(1).
    6. repec:mcb:jmoncb:v:45:y:2013:i::p:535-558 is not listed on IDEAS
    7. Watanabe, Toshiaki & Nakajima, Jouchi, 2023. "High-frequency realized stochastic volatility model," Discussion paper series HIAS-E-127, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    8. Giorgio E. Primiceri, 2005. "Time Varying Structural Vector Autoregressions and Monetary Policy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 821-852.
    9. Marco Del Negro & Giorgio E. Primiceri, 2015. "Time Varying Structural Vector Autoregressions and Monetary Policy: A Corrigendum," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(4), pages 1342-1345.
    10. 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.
    11. Omori, Yasuhiro & Watanabe, Toshiaki, 2008. "Block sampler and posterior mode estimation for asymmetric stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2892-2910, February.
    12. Omori, Yasuhiro & Chib, Siddhartha & Shephard, Neil & Nakajima, Jouchi, 2007. "Stochastic volatility with leverage: Fast and efficient likelihood inference," Journal of Econometrics, Elsevier, vol. 140(2), pages 425-449, October.
    13. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
    14. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
    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. Joshua C. C. Chan, 2017. "The Stochastic Volatility in Mean Model With Time-Varying Parameters: An Application to Inflation Modeling," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 17-28, January.
    2. Koop, Gary & Korobilis, Dimitris, 2010. "Bayesian Multivariate Time Series Methods for Empirical Macroeconomics," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(4), pages 267-358, July.
    3. Yasuhiro Omori & Siddhartha Chib & Neil Shephard & Jouchi Nakajima, 2004. "Stochastic Volatility with Leverage: Fast Likelihood Inference," CIRJE F-Series CIRJE-F-297, CIRJE, Faculty of Economics, University of Tokyo.
    4. Nakajima, Jouchi & Omori, Yasuhiro, 2009. "Leverage, heavy-tails and correlated jumps in stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2335-2353, April.
    5. Diego Ferreira & Andreza Aparecida Palma, 2018. "Inflation And Inflation Uncertainty In Latin America: A Time-Varying Stochastic Volatility In Mean Approach," Anais do XLIV Encontro Nacional de Economia [Proceedings of the 44th Brazilian Economics Meeting] 125, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    6. Omori, Yasuhiro & Chib, Siddhartha & Shephard, Neil & Nakajima, Jouchi, 2007. "Stochastic volatility with leverage: Fast and efficient likelihood inference," Journal of Econometrics, Elsevier, vol. 140(2), pages 425-449, October.
    7. Awijen, Haithem & Ben Zaied, Younes & Nguyen, Duc Khuong & Sensoy, Ahmet, 2020. "Endogenous Financial Uncertainty and Macroeconomic Volatility: Evidence from the United States," MPRA Paper 101276, University Library of Munich, Germany, revised Jun 2020.
    8. Drew Creal & Siem Jan Koopman & Eric Zivot, 2008. "The Effect of the Great Moderation on the U.S. Business Cycle in a Time-varying Multivariate Trend-cycle Model," Tinbergen Institute Discussion Papers 08-069/4, Tinbergen Institute.
    9. Kelly Trinh & Bo Zhang & Chenghan Hou, 2025. "Macroeconomic real‐time forecasts of univariate models with flexible error structures," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 44(1), pages 59-78, January.
    10. Nakajima, Jouchi & Omori, Yasuhiro, 2012. "Stochastic volatility model with leverage and asymmetrically heavy-tailed error using GH skew Student’s t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3690-3704.
    11. Jouchi Nakajima, 2008. "EGARCH and Stochastic Volatility: Modeling Jumps and Heavy-tails for Stock Returns," IMES Discussion Paper Series 08-E-23, Institute for Monetary and Economic Studies, Bank of Japan.
    12. 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.
    13. Joshua C. C. Chan, 2024. "BVARs and stochastic volatility," Chapters, in: Michael P. Clements & Ana Beatriz Galvão (ed.), Handbook of Research Methods and Applications in Macroeconomic Forecasting, chapter 3, pages 43-67, Edward Elgar Publishing.
    14. Shirota, Shinichiro & Hizu, Takayuki & Omori, Yasuhiro, 2014. "Realized stochastic volatility with leverage and long memory," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 618-641.
    15. Chan, Joshua C.C., 2013. "Moving average stochastic volatility models with application to inflation forecast," Journal of Econometrics, Elsevier, vol. 176(2), pages 162-172.
    16. Nakajima, Jouchi & Kasuya, Munehisa & Watanabe, Toshiaki, 2011. "Bayesian analysis of time-varying parameter vector autoregressive model for the Japanese economy and monetary policy," Journal of the Japanese and International Economies, Elsevier, vol. 25(3), pages 225-245, September.
    17. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2018. "Measuring Uncertainty and Its Impact on the Economy," The Review of Economics and Statistics, MIT Press, vol. 100(5), pages 799-815, December.
    18. Jouchi Nakajima, 2011. "Time-Varying Parameter VAR Model with Stochastic Volatility: An Overview of Methodology and Empirical Applications," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 29, pages 107-142, November.
    19. Nakajima, Jouchi & Kunihama, Tsuyoshi & Omori, Yasuhiro & Frühwirth-Schnatter, Sylvia, 2012. "Generalized extreme value distribution with time-dependence using the AR and MA models in state space form," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3241-3259.
    20. Gary Koop & Simon M. Potter, 2007. "A flexible approach to parametric inference in nonlinear time series models," Staff Reports 285, Federal Reserve Bank of New York.

    More about this item

    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:2404.13986. 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.