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MCMC Bayesian Estimation of a Skew-GED Stochastic Volatily Model

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  • Nunzio Cappuccio

    ()
    (Department of Economics (University of Padova))

  • Diego Lubian

    ()
    (University of Economics (University of Verona))

  • Davide Raggi

    ()
    (Department of Statistics (University of Padova))

Abstract

In this paper we present a stochastic volatility model assuming that the return shock has a Skew-GED distribution. This allows a parsimonious yet flexible treatment of asymmetry and heavy tails in the conditional distribution of returns. The Skew-GED distribution nests both the GED, the Skew-normal and the normal densities as special cases so that specification tests are easily performed. Inference is conducted under a Bayesian framework using Markov Chain MonteCarlo methods for computing the posterior distributions of the parameters. More precisely, our Gibbs-MH updating scheme makes use of the Delayed Rejection Metropolis-Hastings methodology as proposed by Tierney and Mira (1999), and of Adaptive-Rejection Metropolis sampling. We apply this methodology to a data set of daily and weekly exchange rates. Our results suggest that daily returns are mostly symmetric with fat-tailed distributions while weekly returns exhibit both significant asymmetry and fat tails.

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Bibliographic Info

Paper provided by University of Verona, Department of Economics in its series Working Papers with number 7.

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Length: 35
Date of creation: Sep 2003
Date of revision:
Handle: RePEc:ver:wpaper:7

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Keywords: Stochastic volatility; Markov Chain MonteCarlo; Skewness; Heavy tails; Bayesian inference; Metropolis-Hastings sampling;

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References

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  1. Antonietta Mira, 2001. "On Metropolis-Hastings algorithms with delayed rejection," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3-4), pages 231-241.
  2. Eric Ghysels & Andrew Harvey & Éric Renault, 1995. "Stochastic Volatility," CIRANO Working Papers, CIRANO 95s-49, CIRANO.
  3. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  4. Siddhartha Chib & Edward Greenberg, 1994. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometrics, EconWPA 9408001, EconWPA, revised 24 Oct 1994.
  5. Mark Steel, 1998. "Bayesian analysis of stochastic volatility models with flexible tails," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 17(2), pages 109-143.
  6. Chunhachinda, Pornchai & Dandapani, Krishnan & Hamid, Shahid & Prakash, Arun J., 1997. "Portfolio selection and skewness: Evidence from international stock markets," Journal of Banking & Finance, Elsevier, Elsevier, vol. 21(2), pages 143-167, February.
  7. Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
  8. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(1), pages 69-87, January.
  9. Roman Liesenfeld & Robert C. Jung, 2000. "Stochastic volatility models: conditional normality versus heavy-tailed distributions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 15(2), pages 137-160.
  10. C.S. Forbes & G.M. Martin & J. Wright, 2002. "Bayesian Estimation of a Stochastic Volatility Model Using Option and Spot Prices," Monash Econometrics and Business Statistics Working Papers, Monash University, Department of Econometrics and Business Statistics 2/02, Monash University, Department of Econometrics and Business Statistics.
  11. Gary Koop & M. F. J. Steel, 2004. "Bayesian Analysis of Stochastic Frontier Models," ESE Discussion Papers, Edinburgh School of Economics, University of Edinburgh 19, Edinburgh School of Economics, University of Edinburgh.
  12. Éric Jacquier & Nicholas G. Polson & Peter E. Rossi, 1995. "Models and Priors for Multivariate Stochastic Volatility," CIRANO Working Papers, CIRANO 95s-18, CIRANO.
  13. Andersen, Torben G, 1996. " Return Volatility and Trading Volume: An Information Flow Interpretation of Stochastic Volatility," Journal of Finance, American Finance Association, American Finance Association, vol. 51(1), pages 169-204, March.
  14. repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
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Citations

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Cited by:
  1. Rydlewski, Jerzy P. & Snarska, Małgorzata, 2014. "On geometric ergodicity of skewed—SVCHARME models," Statistics & Probability Letters, Elsevier, Elsevier, vol. 84(C), pages 192-197.
  2. Ehlers, Ricardo S., 2012. "Computational tools for comparing asymmetric GARCH models via Bayes factors," Mathematics and Computers in Simulation (MATCOM), Elsevier, Elsevier, vol. 82(5), pages 858-867.
  3. Tsiotas, Georgios, 2012. "On generalised asymmetric stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 56(1), pages 151-172, January.
  4. Xiuping Mao & Esther Ruiz & Helena Veiga, 2013. "One for all : nesting asymmetric stochastic volatility models," Statistics and Econometrics Working Papers, Universidad Carlos III, Departamento de Estadística y Econometría ws131110, Universidad Carlos III, Departamento de Estadística y Econometría.
  5. Jerzy P. Rydlewski & Ma{\l}gorzata Snarska, 2012. "On Geometric Ergodicity of Skewed - SVCHARME models," Papers 1209.1544, arXiv.org.
  6. Trojan, Sebastian, 2013. "Regime Switching Stochastic Volatility with Skew, Fat Tails and Leverage using Returns and Realized Volatility Contemporaneously," Economics Working Paper Series 1341, University of St. Gallen, School of Economics and Political Science, revised Aug 2014.

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