Before revision:  This is a strong argument to claim that observed variations of multifractality in financial time series are to be ascribed to a structural breakdown in the temporal covariance structure of stock returns series. As a consequence, multi fractal models with a constant intermittency parameter may not always be satisfactory in reproducing financial market behaviour .
After revision:  We test these hypotheses of constant multifractality considering different specifications of MRW model with fatter tails: in all cases considered, although the thickness of the tails accounts for most of anomalous fluctuations of multifractality, still cannot fully explain the observed fluctuations .