A double-threshold GARCH model for the French Franc/Deutschmark exchange rate

This paper combines and generalizes a number of recent time series models o f daily exchange rate series by using a SETAR model which also allows the v ariance equation of a GARCH specification for the error terms to be drawn f rom more than one regime. An application of the model to the French Franc/D eutschmark exchange rate demonstrates that out-of-sample forecasts for the exchange rate volatility are also improved when the restriction that the da ta it is drawn from a single regime is removed. This result highlights the importance of considering both types of regime shift (i.e. thresholds in va riance as well as in mean) when analysing financial time series. Copyright (C) 2001 John Wiley & Sons, Ltd.