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

Abstract

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 Ludeña [Ann. Appl. Probab. 18 (2008) 1138-1163]. 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.

Published in at http://dx.doi.org/10.3150/12-BEJ489 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (4)

• Central limit theorems for sequences of multiple stochastic integrals
• Log-infinitely divisible multifractal processes
• Multifractal stationary random measures and multifractal random walks with log-infinitely divisible scaling laws
• $L^p$-variations for multifractal fractional random walks

Cited by in corpus (2)

• Assessing Relative Volatility/Intermittency/Energy Dissipation
• Coupled uncertainty provided by a multifractal random walker