We report evidence that empirical data show time varying multifractal properties. This is obtained by comparing empirical observations of the weighted generalised Hurst exponent (wGHE) with time series simulated via Multifractal Random Walk (MRW) by Bacry et al. [E.Bacry, J.Delour and J.Muzy, Phys.Rev.E \,{\bf 64 026103, 2001}]. While dynamical wGHE computed on synthetic MRW series is consistent with a scenario where multifractality is constant over time, fluctuations in the dynamical wGHE observed in empirical data fail to be in agreement with a MRW with constant intermittency parameter. 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 .
We perform an extensive empirical analysis of scaling properties of equity returns, suggesting that financial data show time varying multifractal properties. This is obtained by comparing empirical observations of the weighted generalised Hurst exponent (wGHE) with time series simulated via Multifractal Random Walk (MRW) by Bacry et al. [E.Bacry, J.Delour and J.Muzy, Phys.Rev.E \,{\bf 64 026103, 2001}]. While dynamical wGHE computed on synthetic MRW series is consistent with a scenario where multifractality is constant over time, fluctuations in the dynamical wGHE observed in empirical data are not in agreement with a MRW with constant intermittency parameter. 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 .
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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
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