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

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  • 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)

Abstract

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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Bibliographic Info

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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  1. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
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  3. Sangjoon Kim, Neil Shephard & Siddhartha Chib, . "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers W26, revised version of W, Economics Group, Nuffield College, University of Oxford.
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  8. 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.
  9. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "Exchange Rate Returns Standardized by Realized Volatility Are (Nearly) Gaussian," Center for Financial Institutions Working Papers 00-29, Wharton School Center for Financial Institutions, University of Pennsylvania.
  10. Epps, Thomas W & Epps, Mary Lee, 1976. "The Stochastic Dependence of Security Price Changes and Transaction Volumes: Implications for the Mixture-of-Distributions Hypothesis," Econometrica, Econometric Society, vol. 44(2), pages 305-21, March.
  11. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
  12. Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, vol. 51(2), pages 485-505, March.
  13. 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.
  14. 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.
  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. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
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Cited by:
  1. repec:hal:cesptp:halshs-00179325 is not listed on IDEAS
  2. Lars Forsberg & Anders Eriksson, 2004. "The Mean Variance Mixing GARCH (1,1) model," Econometric Society 2004 Australasian Meetings 323, Econometric Society.
  3. Peter Reinhard Hansen & Zhuo Huang, 2012. "Exponential GARCH Modeling with Realized Measures of Volatility," Economics Working Papers ECO2012/26, European University Institute.
  4. Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006. "Option valuation with conditional skewness," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 253-284.
  5. repec:hal:journl:halshs-00179325 is not listed on IDEAS
  6. Peter Christoffersen & Bruno Feunou & Kris Jacobs & Nour Meddahi, 2012. "The Economic Value of Realized Volatility: Using High-Frequency Returns for Option Valuation," Working Papers 12-34, Bank of Canada.
  7. Andersen, Torben G. & Bollerslev, Tim & Dobrev, Dobrislav, 2007. "No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects, jumps and i.i.d. noise: Theory and testable distributional implications," Journal of Econometrics, Elsevier, vol. 138(1), pages 125-180, May.
  8. Makoto Takahashi & Yasuhiro Omori & Toshiaki Watanabe, 2007. "Estimating Stochastic Volatility Models Using Daily Returns and Realized Volatility Simultaneously ( Revised in March 2008; Published in "Computational Statistics and Data Analysis", 53-6, 2," CARF F-Series CARF-F-108, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  9. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling and Forecasting of Return Volatility," CREATES Research Papers 2007-18, School of Economics and Management, University of Aarhus.
  10. Bertrand B. Maillet & Jean-Philippe R. Médecin, 2010. "Extreme Volatilities, Financial Crises and L-moment Estimations of Tail-indexes," Working Papers 2010_10, Department of Economics, University of Venice "Ca' Foscari".
  11. Tim Bollerslev & Uta Kretschmer & Christian Pigorsch & George Tauchen, 2010. "A Discrete-Time Model for Daily S&P500 Returns and Realized Variations: Jumps and Leverage Effects," Working Papers 10-06, Duke University, Department of Economics.
  12. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2003. "Some Like it Smooth, and Some Like it Rough: Untangling Continuous and Jump Components in Measuring, Modeling, and Forecasting Asset Return Volatility," PIER Working Paper Archive 03-025, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Sep 2003.
  13. 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.
  14. Anastassios A. Drakos & Georgios P. Kouretas & Leonidas P. Zarangas, 2010. "Forecasting financial volatility of the Athens stock exchange daily returns: an application of the asymmetric normal mixture GARCH model," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 15(4), pages 331-350.
  15. Matei, Marius, 2010. "Risk analysis in the evaluation of the international investment opportunities. Advances in modelling and forecasting volatility for risk assessment purposes," Working Papers of Institute for Economic Forecasting 100201, Institute for Economic Forecasting.

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