Estimating the scaling function of multifractal measures and multifractal random walks using ratios. (English) Zbl 1398.60059
Summary: 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 the first author [Ann. Appl. Probab. 18, No. 3, 1138–1163 (2008; Zbl 1154.60029)]. 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.
MSC:
| 60G22 | Fractional processes, including fractional Brownian motion |
| 60F05 | Central limit and other weak theorems |
| 60G57 | Random measures |
| 62G05 | Nonparametric estimation |
Citations:
Zbl 1154.60029References:
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