Bridging the gap between the distribution of realized (ECU) volatility and ARCH modelling (of the Euro): the GARCH‐NIG model
基于ECU篮子货币兑美元的五分钟高频数据，发现已实现波动率近似逆高斯分布，而经其标准化的日收益率近似正态分布，并构建GARCH-NIG模型对欧元/美元汇率进行样本外预测，效果准确。
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.