P. Abry, Y. Malevergne, H. Wendt, M. Senneret, L. Jaffrès, B. Laustriat
Multifractal analysis has become a standard signal processing tool used successfully to model scale-invariant time dynamics in many different fields. This is notably the case in financial engineering where, after the valuable contributions of Mandelbrot, multifractal models have been used since the end of the 1990s to describe the time fluctuations of asset prices. However, the exact characteristics of the temporal dynamics that are actually encoded in the multifractal properties are usually only partially understood. In finance, in particular, multifractality is associated with the clustering of large excursions of returns, but its relationship with trends (signs of returns) or volatility (modulus of returns) remains unclear.
Comparing the estimated multifractal properties of well-controlled synthetic multifractal processes to those of proxy data, obtained by applying random permutations (shuffling) either to the signs or to the modulus or to both, on the increments of the original data, provides a better understanding of which aspects of the time dynamics are captured by multifractality. The same procedure applied to a large dataset of asset prices composing the STOXX® Europe 600 index allows us to highlight a simple and robust relationship between multifractality and volatility, and a weaker and more complex relationship with returns.
This paper was published as part of EUSIPCO 2019, 27th European Signal Processing Conference.