Determining Local Singularity Strengths and their Spectra with the Wavelet Transform

We present a robust method of estimating the effective strength of singularities (the effective Hoelder exponent) locally at an arbitrary resolution. The method is motivated by the multiplicative cascade paradigm, and implemented on the hierarchy of singularities revealed with the wavelet transform modulus maxima tree. In addition, we illustrate the direct estimation of the scaling spectrum of the effective singularity strength, and we link it to the established partition function based multifractal formalism. We motivate both the local and the global multifractal analysis by showing examples of computer generated and real life time series.