Abstract
A semiparametric extension of the GJR model (Glosten et al., 1993. Journal of Finance 48,
1779–1801) is proposed for the volatility of foreign exchange returns. Under reasonable
assumptions, asymptotic normal distributions are established for the estimators of the model,
corroborated by simulation results. When applied to the Deutsche Mark/US Dollar and the
Deutsche Mark/British Pound daily returns data, the semiparametric volatility model
outperforms the GJR model as well as the more commonly used GARCH(1; 1) model in
terms of goodness-of-fit, and forecasting, by correcting overgrowth in volatility.