Modelling Exchange Rates Volatility with Multivariate Long-Memory ARCH Processes

We propose twp multivariate long-memory ARCH models, which extend the univariate long-memory models by Ding and Granger (1996) and Baillie, Bollerslev and Mikkelsen (1996). We consider a long-memory extension of the restricted constant conditional correlations (CCC) model introduced by Bollerslev (1990), and an unrestricted conditional covariance matrix model. We apply these two models to two daily returns on exchanges rates series, the Pound-US dollar, and the Deutschmark-US dollar. the estimation results for both models show: (i) that the unrestricted model outperforms the restricted CCC model, and (ii) that all the elements of the conditional covariance matrix share the same degree of long-memory for the period April 1979-January 1997. However, this result does not hold for the floating periods MArch 1973-JAnuary 1997 and September 1971-JAnuary 1997. This break in the long-term structure may be caused by the European Monetary System inception in March 1979.