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

Author

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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.

Suggested Citation

  • 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.
    • Handle: RePEc:jae:japmet:v:17:y:2002:i:5:p:535-548
    DOI: 10.1002/jae.685
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    References listed on IDEAS

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