Non stationary multifractality in stock returns

TL;DR

This paper investigates the time-varying multifractal properties of stock returns, revealing that empirical data exhibit non-stationary multifractality not fully explained by existing models.

Contribution

It demonstrates that standard multifractal models with constant intermittency cannot fully capture the observed fluctuations in stock return multifractality.

Findings

Empirical stock returns show non-stationary multifractal behavior.

Synthetic models with constant parameters do not replicate observed fluctuations.

Fat tails contribute to, but do not fully explain, multifractality fluctuations.

Abstract

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 \textit{et al.} [\textit{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.