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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(s) -
Forsberg Lars,
Bollerslev Tim
Publication year - 2002
Publication title -
journal of applied econometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.878
H-Index - 99
eISSN - 1099-1255
pISSN - 0883-7252
DOI - 10.1002/jae.685
Subject(s) - autoregressive conditional heteroskedasticity , econometrics , inverse gaussian distribution , volatility (finance) , economics , gaussian , liberian dollar , realized variance , us dollar , normal distribution , distribution (mathematics) , mathematics , statistics , exchange rate , monetary economics , finance , physics , mathematical analysis , quantum mechanics
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.