2011/02/28 by Carenne Ludeña, Philippe Soulier
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #Estimator #Financial Risk and Volatility Modeling #Function (biology) #Limit (mathematics) #Logarithm #Mathematical Dynamics and Fractals #Multifractal system #Random walk #Scaling #math.ST #stat.TH
paper · pdf · doi:10.3150/12-bej489
published as Bernoulli 20, 1 (2014) 334-376 · 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)
openalex publication_date 2014/01/22 · arxiv created 2014/02/05 · arxiv updated 2014/04/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.