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Stochastic Volatility in Mean Models with Heavy Tails: A Fast Approximate Bayesian Inference Using Hidden Markov Models

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Listed:
  • Bruno E. Holtz
  • Carlos A. Abanto-Valle
  • Ricardo S. Ehlers
  • Gabriel Rodr'iguez

Abstract

This paper extends the approximate Bayesian estimation framework for Stochastic Volatility in Mean (SVM) models to accommodate heavy-tailed distributions from the Scale Mixture of Normals (SMN) family. To overcome the computational challenges arising from these models, we propose a numerically stable estimation procedure that exploits special functions to eliminate the need for direct numerical integration. Furthermore, the implementation incorporates parallel computing strategies that substantially reduce computational costs. Simulation studies and empirical applications demonstrate that the proposed approach delivers accurate inference while achieving computational times that are approximately an order of magnitude smaller than those required by conventional Markov chain Monte Carlo (MCMC) methods.

Suggested Citation

  • Bruno E. Holtz & Carlos A. Abanto-Valle & Ricardo S. Ehlers & Gabriel Rodr'iguez, 2026. "Stochastic Volatility in Mean Models with Heavy Tails: A Fast Approximate Bayesian Inference Using Hidden Markov Models," Papers 2606.22615, arXiv.org.
    • Handle: RePEc:arx:papers:2606.22615
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    References listed on IDEAS

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    2. Carlos A. Abanto-Valle & Hernán B. Garrafa-Aragón, 2019. "Threshold Stochastic Volatility Models with Heavy Tails:A Bayesian Approach," Revista Economía, Fondo Editorial - Pontificia Universidad Católica del Perú, vol. 42(83), pages 32-53.
    3. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    4. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    5. Mark Girolami & Ben Calderhead, 2011. "Riemann manifold Langevin and Hamiltonian Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(2), pages 123-214, March.
    6. Nadarajah, Saralees & Kotz, Samuel, 2006. "R Programs for Truncated Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 16(c02).
    7. Didit Nugroho & Takayuki Morimoto, 2015. "Estimation of realized stochastic volatility models using Hamiltonian Monte Carlo-Based methods," Computational Statistics, Springer, vol. 30(2), pages 491-516, June.
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