We overview the notion of regular scaling in data and estimators of this regular scaling on several examples involving high frequency measurements. Next we discuss the importance of wavelet domains and ability of wavelets to precisely estimate regular
scaling (monofractality) and some deviations from regular scaling (time-dependent Hursts, multifractality, etc).
The convex rearrangements are introduced and basic results discussed. The convex rearrangements in the wavelet domain lead to a multiplicity of estimators of a Hurst
exponent, which brings an interesting issue of designing the best estimator.