An investigation of long range dependence in intra-day foreign exchange rate volatility

A comprehensive set of estimates of long memory in the volatility of three intra-day foreign exchange data series is presented. Robust semiparametric methods are used. Deseasonalizing procedures are proposed and permit the use of fully parametric methods which provide efficient tests of long memory. The hypothesis of long range dependence in the raw returns is rejected. In the volatility series, however, there is evidence of a long range dependent component, a finding which is significant and consistent across currencies. Furthermore, the hypothesis of I(1) volatility is strongly rejected in favour of a covariance stationary alternative, with evidence that previous findings of near-integrated volatility are due to the omission of long-range dependent components.