Modelling Exchange Rates Volatility with Multivariate LongMemory ARCH Processes by Gilles Teyssiere

This revised version September We consider two multivariate longmemory ARCH models which extend the univariate longmemory ARCH models we rst consider a longmemory extension of the restricted con stant conditional correlations CCC model introduced by Bollerslev and we propose a new unrestricted conditional covariance matrix model which models the conditional covari ances as longmemory ARCH processes We apply these two models to two daily returns on foreign exchanges FX rates series the PoundUS dollar and the DeutschmarkUS 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 longmemory for the period April January However this result does not hold for the oating periods Marc