Numerical methods for the estimation of multifractal singularity spectra on sampled data: A comparative study

Physical variables in scale invariant systems often show chaotic, turbulent-like behaviour, what is commonly associated to the existence of a fractal or multifractal underlying structure. The detection of such structure over experimental data requires appropriate methods of analysis and to establish criteria to measure the confidence degree in the estimates. In this paper we will test four different techniques for the evaluation of the multifractal singularity spectrum, validating them over a benchmark of synthetically generated multifractal 1D signals. We will compare the results, discussing on the adequacy of each method according to the context.