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On the Normal Inverse Gaussian Stochastic Volatility Model

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  • Andersson, Jonas

Abstract

In this article, the normal inverse Gaussian stochastic volatility model of Barndorf-Nielsen is extended. The resulting model has a more flexible lag structure than the original one. In addition, the second- and fourth-order moments, important properties of a volatility model, are derived. The model can be considered either as a generalized autoregressive conditional heteroscedasticity model with nonnormal errors or as a stochastic volatility model with an inverse Gaussian distributed conditional variance. A simulation study is made to investigate the performance of the maximum likelihood estimator of the model. Finally, the model is applied to stock returns and exchange-rate movements. Its fit to two stylized facts and its forecasting performance is compared with two other volatility models.

Suggested Citation

  • Andersson, Jonas, 2001. "On the Normal Inverse Gaussian Stochastic Volatility Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 44-54, January.
  • Handle: RePEc:bes:jnlbes:v:19:y:2001:i:1:p:44-54
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    Cited by:

    1. Nikolaus Hautsch & Stefan Voigt, 2017. "Large-Scale Portfolio Allocation Under Transaction Costs and Model Uncertainty," Papers 1709.06296, arXiv.org.
    2. Malmsten, Hans & Teräsvirta, Timo, 2004. "Stylized Facts of Financial Time Series and Three Popular Models of Volatility," SSE/EFI Working Paper Series in Economics and Finance 563, Stockholm School of Economics, revised 03 Sep 2004.
    3. Jouchi Nakajima & Yasuhiro Omori, 2010. "Stochastic Volatility Model with Leverage and Asymmetrically Heavy-Tailed Error Using GH Skew Student's t-Distribution Models," CIRJE F-Series CIRJE-F-738, CIRJE, Faculty of Economics, University of Tokyo.
    4. Yang Minxian, 2011. "Volatility Feedback and Risk Premium in GARCH Models with Generalized Hyperbolic Distributions," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(3), pages 1-21, May.
    5. Lars Forsberg & Anders Eriksson, 2004. "The Mean Variance Mixing GARCH (1,1) model," Econometric Society 2004 Australasian Meetings 323, Econometric Society.
    6. Ruiz, Esther & Veiga, Helena, 2008. "Modelling long-memory volatilities with leverage effect: A-LMSV versus FIEGARCH," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2846-2862, February.
    7. Shiyi Chen & Wolfgang K. Härdle & Kiho Jeong, 2010. "Forecasting volatility with support vector machine-based GARCH model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(4), pages 406-433.
    8. Rehim Kilic, 2011. "A conditional variance tale from an emerging economy's freely floating exchange rate," Applied Economics, Taylor & Francis Journals, vol. 43(19), pages 2465-2480.
    9. Fiszeder, Piotr & Perczak, Grzegorz, 2016. "Low and high prices can improve volatility forecasts during periods of turmoil," International Journal of Forecasting, Elsevier, vol. 32(2), pages 398-410.
    10. Walter Krämer & Philip Mess, 2012. "Structural Change and Spurious Persistence in Stochastic Volatility," Ruhr Economic Papers 0310, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    11. Guo, Zi-Yi, 2017. "Empirical Performance of GARCH Models with Heavy-tailed Innovations," EconStor Preprints 167626, ZBW - German National Library of Economics.
    12. N. Balakrishna & Bovas Abraham & Ranjini Sivakumar, 2006. "Gamma stochastic volatility models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(3), pages 153-171.
    13. 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.
    14. Patricia Lengua & Cristian Bayes & Gabriel Rodríguez, 2015. " A Stochastic Volatility Model with GH Skew Student’s t-Distribution: Application to Latin-American Stock Returns," Documentos de Trabajo / Working Papers 2015-405, Departamento de Economía - Pontificia Universidad Católica del Perú.
    15. Nakajima Jouchi, 2013. "Stochastic volatility model with regime-switching skewness in heavy-tailed errors for exchange rate returns," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(5), pages 499-520, December.
    16. Krämer, Walter & Messow, Philip, 2012. "Structural Change and Spurious Persistence in Stochastic Volatility," Ruhr Economic Papers 310, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    17. Lars Forsberg & Tim Bollerslev, 2002. "Bridging the gap between the distribution of realized (ECU) volatility and ARCH modelling (of the Euro): the GARCH-NIG model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 535-548.
    18. Lars Stentoft, 2008. "American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(4), pages 540-582, Fall.
    19. Pentti Saikkonen & Markku Lanne, 2004. "A Skewed GARCH-in-Mean Model: An Application to U.S. Stock Returns," Econometric Society 2004 North American Summer Meetings 469, Econometric Society.
    20. Homm, Ulrich & Pigorsch, Christian, 2012. "Beyond the Sharpe ratio: An application of the Aumann–Serrano index to performance measurement," Journal of Banking & Finance, Elsevier, vol. 36(8), pages 2274-2284.
    21. repec:zbw:rwirep:0310 is not listed on IDEAS

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