Nonlinear dependence in British pound exchange rates

The Brock, Dechert and Scheinkman (1987) method is used to test for nonlinear dependence in daily rates of change of the exchange rate of the British pound relative to seven most heavily traded currencies against the pound during the period 2 January 1993 to 7 October 1996. The currencies are the US dollar, the Deutsche mark, the French franc, the Swiss franc, the Canadian dollar, the Japanese yen and the Italian lira. The results suggest that nonlinear dependence exists in all seven British pound exchange rates. Except for the US dollar, nonlinear dependence is due to nonlinearity in the variance and is captured by a GARCH(1,1)-t model. For the US dollar, nonlinear dependence is due to nonlinearity both in the mean and the variance and is captured by a GARCH-in-mean (GARCH-M) model.