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Bridging the gap between the distribution of realized (ECU) volatility and ARCH modelling (of the Euro): the GARCH-NIG model

  • Lars Forsberg

    (Department of Information Science, Division of Statistics, Uppsala University, Sweden)

  • Tim Bollerslev

    (Department of Economics and Finance, Duke University, NC, USA and NBER)

This paper bridges the gap between traditional ARCH modelling and recent advances on realized volatilities. Based on a ten-year sample of five-minute returns for the ECU basket currencies versus the US dollar, we find that the realized volatilities constructed from the summation of the high-frequency intraday squared returns conditional on the lagged squared daily returns are approximately Inverse Gaussian (IG) distributed, while the distribution of the daily returns standardized by their realized volatilities is approximately normal. Moreover, the implied daily GARCH model with Normal Inverse Gaussian (NIG) errors estimated for the ECU returns results in very accurate out-of-sample predictions for the three years of actual daily Euro|US dollar exchange rates. Copyright © 2002 John Wiley & Sons, Ltd.

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File URL: http://hdl.handle.net/10.1002/jae.685
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Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 17 (2002)
Issue (Month): 5 ()
Pages: 535-548

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Handle: RePEc:jae:japmet:v:17:y:2002:i:5:p:535-548
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  4. Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 361-93, July.
  5. Shiqing Ling & Michael McAleer, 2001. "Necessary and Sufficient Moment Conditions for the GARCH(r,s) and Asymmetric Power GARCH(r,s) Models," ISER Discussion Paper 0534, Institute of Social and Economic Research, Osaka University.
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  7. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2000. "Exchange Rate Returns Standardized by Realized Volatility are (Nearly) Gaussian," NBER Working Papers 7488, National Bureau of Economic Research, Inc.
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  15. 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.
  16. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2002. "Parametric and Nonparametric Volatility Measurement," NBER Technical Working Papers 0279, National Bureau of Economic Research, Inc.
  17. Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, vol. 51(2), pages 485-505, March.
  18. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "How accurate is the asymptotic approximation to the distribution of realised volatility?," Economics Papers 2001-W16, Economics Group, Nuffield College, University of Oxford.
  19. Andersen, Torben G, 1996. " Return Volatility and Trading Volume: An Information Flow Interpretation of Stochastic Volatility," Journal of Finance, American Finance Association, vol. 51(1), pages 169-204, March.
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