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The smooth transition autoregressive target zone model with the Gaussian stochastic volatility and TGARCH error terms with applications

Author

Listed:
  • Oleg Korenok

    (Department of Economics, VCU School of Business)

  • Stanislav Radchenko

    (Department of Economics, University of North Carolina at Charlotte)

Abstract
This paper proposes to model the error term in smooth transition autoregressive target zone model as Gaussian with stochastic volatility (STARTZ-SV) or as Student-t with GARCH volatility (STARTZ-TGARCH). Using the dynamics of Norwegian krone exchange rate index, we show that both models produce standardized residuals that are closer to assumed distributions and do not produce a hump in the estimated marginal distribution of exchange rate which is more consistent with theoretical predictions. We apply developed models to test whether the dynamics of oil price can be well approximated by the Krugman’s target zone model. Our estimates of conditional volatility and marginal distribution reject the target zone hypothesis.

Suggested Citation

  • Oleg Korenok & Stanislav Radchenko, 2005. "The smooth transition autoregressive target zone model with the Gaussian stochastic volatility and TGARCH error terms with applications," Working Papers 0505, VCU School of Business, Department of Economics.
    • Handle: RePEc:vcu:wpaper:0505
    as

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    References listed on IDEAS

    as
    1. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    2. Catherine S. Forbes & Paul Kofman, 2000. "Bayesian Target Zones," Research Paper Series 32, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Mundaca, B. Gabriela, 2001. "Central bank interventions and exchange rate band regimes," Journal of International Money and Finance, Elsevier, vol. 20(5), pages 677-700, October.
    4. John Geweke, 1994. "Bayesian comparison of econometric models," Working Papers 532, Federal Reserve Bank of Minneapolis.
    5. 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.
    6. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    7. 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.
    8. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 145-175.
    9. Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 375-400.
    10. Li, Kai, 1999. "Exchange Rate Target Zone Models: A Bayesian Evaluation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 461-490, Sept.-Oct.
    11. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
    12. Sarno,Lucio & Taylor,Mark P., 2003. "The Economics of Exchange Rates," Cambridge Books, Cambridge University Press, number 9780521485845.
    13. Bekaert, Geert & Gray, Stephen F., 1998. "Target zones and exchange rates:: An empirical investigation," Journal of International Economics, Elsevier, vol. 45(1), pages 1-35, June.
    14. Alhajji, A. F. & Huettner, David, 2000. "OPEC and other commodity cartels: a comparison," Energy Policy, Elsevier, vol. 28(15), pages 1151-1164, December.
    15. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 247-264.
    16. Lundbergh, Stefan & Terasvirta, Timo & van Dijk, Dick, 2003. "Time-Varying Smooth Transition Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 104-121, January.
    17. Lundbergh, Stefan & Terasvirta, Timo, 2006. "A time series model for an exchange rate in a target zone with applications," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 579-609.
    18. Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
    19. 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.
    20. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Univariate and multivariate stochastic volatility models: estimation and diagnostics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 505-531, September.
    21. Paul R. Krugman, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(3), pages 669-682.
    22. Bai, Xuezheng & Russell, Jeffrey R. & Tiao, George C., 2003. "Kurtosis of GARCH and stochastic volatility models with non-normal innovations," Journal of Econometrics, Elsevier, vol. 114(2), pages 349-360, June.
    23. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    24. Jun Yu, 2002. "Forecasting volatility in the New Zealand stock market," Applied Financial Economics, Taylor & Francis Journals, vol. 12(3), pages 193-202.
    25. Ruiz, Esther, 1994. "Quasi-maximum likelihood estimation of stochastic volatility models," Journal of Econometrics, Elsevier, vol. 63(1), pages 289-306, July.
    26. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
    27. Luc Bauwens & Michel Lubrano, 1998. "Bayesian inference on GARCH models using the Gibbs sampler," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages 23-46.
    28. Esfandiar Maasoumi & Michael McAleer, 2006. "Multivariate Stochastic Volatility: An Overview," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 139-144.
    29. Robert Sollis & Stephen Leybourne & Paul Newbold, 1999. "Unit Roots and Asymmetric Smooth Transitions," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(6), pages 671-677, November.
    30. Jacquier, Eric & Polson, Nicholas G. & Rossi, P.E.Peter E., 2004. "Bayesian analysis of stochastic volatility models with fat-tails and correlated errors," Journal of Econometrics, Elsevier, vol. 122(1), pages 185-212, September.
    31. M. Angeles Carnero, 2004. "Persistence and Kurtosis in GARCH and Stochastic Volatility Models," Journal of Financial Econometrics, Oxford University Press, vol. 2(2), pages 319-342.
    32. Tang, Linghui & Hammoudeh, Shawkat, 2002. "An empirical exploration of the world oil price under the target zone model," Energy Economics, Elsevier, vol. 24(6), pages 577-596, November.
    33. Kees G. Koedijk & Philip A. Stork & Casper G. De Vries, 1998. "An EMS target zone model in discrete time," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(1), pages 31-48.
    34. Stephen M. Horan, Jeffrey H. Peterson, and James Mahar, 2004. "Implied Volatility of Oil Futures Options Surrounding OPEC Meetings," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3), pages 103-126.
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    More about this item

    Keywords

    target zone; oil price; exchange rate; stochastic volatility; griddy Gibbs; smooth transition;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • Q38 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation - - - Government Policy (includes OPEC Policy)
    • F31 - International Economics - - International Finance - - - Foreign Exchange

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