  The properties of statistical tests for hypotheses concerning the parameters
of the multifractal model of asset returns (MMAR) are investigated, using Monte
Carlo techniques. We show that, in the presence of multifractality,
conventional tests of long memory tend to over-reject the null hypothesis of no
long memory. Our test addresses this issue by jointly estimating long memory
and multifractality. The estimation and test procedures are applied to exchange
rate data for 12 currencies. In 11 cases, the exchange rate returns are
accurately described by compounding a NIID series with a multifractal
time-deformation process. There is no evidence of long memory.
