Estimating the scaling function of multifractal measures and multifractal random walks using ratios

Details Estimating the scaling function of multifractal measures and multifractal random walks using ratios Estimating the scaling function of multifractal measures and multifractal random walks using ratios

2011-02-25

arxiv.org/abs/1102.5176v1

Mathematics

Statistics Theory

Scientific paper

In this paper we prove central limit theorems for bias reduced estimators of the structure function of several multifractal processes, namely mutiplicative cascades, multifractal random measures, multifractal random walk and multifractal fractional random walk as defined by Ludena (2008). Previous estimators of the structure functions considered in the literature were severely biased with a logarithmic rate of convergence, whereas the estimators considered here have a polynomial rate of convergence.

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