Finite nonparametric GARCH model for foreign exchange volatility

GARCH model has been commonly used to describe the volatility of foreign exchange returns, which typically depends on returns many lags before. White the GARCH model provides a simple geometric decaying structure for persistence in time, it restricts the impact of variables to quadratic functions. A finite nonparametric GARCH model is proposed that allows the variables' impact to be a smooth function of any form. A direct local polynomial estimation method for this finite GARCH model is proposed based on results on proportional additive model, and is applied to the German Mark (DEM)/US Dollar (USD) daily returns data. Estimators of both the decaying rate and the impact function are obtained. Diagnostics show satisfactory out-of-sample prediction based on the proposed model, which helps to better understand the dynamics of foreign exchange volatility.