2008/05/26 by Carenne Ludeña · 1 citation
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #Financial Risk and Volatility Modeling #Stochastic processes and financial applications #math.PR #msc:60E07 #msc:60F05 #msc:60G15 #msc:60G18 #msc:60G57 #msc:60K40 #msc:62F10
paper · pdf · doi:10.1214/07-aap483
published as Annals of Applied Probability 2008, Vol. 18, No. 3, 1138-1163 · Published in at http://dx.doi.org/10.1214/07-AAP483 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2008/05/26 · arxiv created 2008/06/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
A multifractal random walk (MRW) is defined by a Brownian motion subordinated by a class of continuous multifractal random measures M[0, t], 0≤t≤1. In this paper we obtain an extension of this process, referred to as multifractal fractional random walk (MFRW), by considering the limit in distribution of a sequence of conditionally Gaussian processes. These conditional processes are defined as integrals with respect to fractional Brownian motion and convergence is seen to hold under certain conditions relating the self-similarity (Hurst) exponent of the fBm to the parameters defining the multifractal random measure M. As a result, a larger class of models is obtained, whose fine scale (scaling) structure is then analyzed in terms of the empirical structure functions. Implications for the analysis and inference of multifractal exponents from data, namely, confidence intervals, are also provided.