Modelling exchange rates: long-run dependence versus conditional heteroscedasticity

Indications for two different features not captured by low-order linear time-series models can be found in day-to-day changes of exchange rates: long memory and conditional heteroscedasticity. These characteristics have inspired the development of ARFIMA and GARCH models. By means of Monte Carlo simulation, it is demonstrated that either of the two features stands a non-negligible chance of being detected spuriously in the presence of the other. A table of explicit empirical small-sample quantiles for identification of long-memory structures in the presence of GARCH effects is included.