Analysis of H-sssi processes using the crossing tree: An alternative to wavelets

In this study we use the crossing tree of a signal for the purpose of analysis of H-sssi processes. The crossing tree performs an ad-hoc decomposition of a signal adapted to its dynamics, and represents a natural tool for the analysis of its local fluctuations. We present here a new multifractal formalism and a novel approach for estimating the spectrum of singularities of H-sssi processes using the crossing-tree. The performance of the crossing-tree based method is demonstrated in a numerical study. Its performance is also compared with state-of-the-art techniques based on wavelets, including wavelet-leaders.