Crossing-tree partition functions

A new multifractal formalism based on the crossing-tree for H-sssi processes was recently introduced [1, 2]. The crossing-tree performs an ad-hoc decomposition of a signal based on its fluctuations, and thus represents a natural tool for the multifractal analysis of time series. The estimation of the Hausdorff spectrum happens in the context of a multifractal formalism, where the spectrum is obtained from a transform of a partition function. In this contribution, we introduce a new crossing-tree partition function, which differs from the original one presented in [2]. We show numerically that the new partition function improves the stability of the estimation in many cases, compared with the original crossing-tree partition function. Estimation is further compared with state-of-the-art techniques, including wavelet and wavelet leaders.