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Efficient Bayesian Inference in Generalized Inverse Gamma Processes for Stochastic Volatility

Listed author(s):
  • Roberto Leon-Gonzalez

    ()

    (National Graduate Institute for Policy Studies (GRIPS) and The Rimini Centre for Economic Analysis (RCEA))

This paper develops a novel and efficient algorithm for Bayesian inference in inverse Gamma Stochastic Volatility models. It is shown that by conditioning on auxiliary variables, it is possible to sample all the volatilities jointly directly from their posterior conditional density, using simple and easy to draw from distributions. Furthermore, this paper develops a generalized inverse Gamma process with more flexible tails in the distribution of volatilities, which still allows for simple and efficient calculations. Using several macroeconomic and financial datasets, it is shown that the inverse Gamma and Generalized inverse Gamma processes can greatly outperform the commonly used log normal volatility processes with student-t errors.

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File URL: http://www.rcea.org/RePEc/pdf/wp19_14.pdf
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Paper provided by The Rimini Centre for Economic Analysis in its series Working Paper Series with number 19_14.

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Date of creation: Sep 2014
Handle: RePEc:rim:rimwps:19_14
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  1. Devroye, Luc, 2002. "Simulating Bessel random variables," Statistics & Probability Letters, Elsevier, vol. 57(3), pages 249-257, April.
  2. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
  3. Jensen, Mark J. & Maheu, John M., 2010. "Bayesian semiparametric stochastic volatility modeling," Journal of Econometrics, Elsevier, vol. 157(2), pages 306-316, August.
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  11. K. Triantafyllopoulos, 2012. "Multiā€variate stochastic volatility modelling using Wishart autoregressive processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(1), pages 48-60, 01.
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  18. repec:bla:restud:v:65:y:1998:i:3:p:361-93 is not listed on IDEAS
  19. Gareth O. Roberts & Omiros Papaspiliopoulos & Petros Dellaportas, 2004. "Bayesian inference for non-Gaussian Ornstein-Uhlenbeck stochastic volatility processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 369-393.
  20. Durham, Garland B., 2007. "SV mixture models with application to S&P 500 index returns," Journal of Financial Economics, Elsevier, vol. 85(3), pages 822-856, September.
  21. 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.
  22. Griffin, J.E. & Steel, M.F.J., 2011. "Stick-breaking autoregressive processes," Journal of Econometrics, Elsevier, vol. 162(2), pages 383-396, June.
  23. Alexander Philipov & Mark Glickman, 2006. "Factor Multivariate Stochastic Volatility via Wishart Processes," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 311-334.
  24. Mark Steel, 1998. "Bayesian analysis of stochastic volatility models with flexible tails," Econometric Reviews, Taylor & Francis Journals, vol. 17(2), pages 109-143.
  25. 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.
  26. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
  27. Satya Dubey, 1970. "Compound gamma, beta and F distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 16(1), pages 27-31, December.
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