ISSN: 1532-6349 print/1532-4214 online DOI: 10.1080/15326340600820505

In this paper we present a novel method for the construction of a stochastic process whose multifractal spectrum has been prescribed. The main idea of the construction is to choose a suitable time-change reparametrizing the time of a fractional Brownian motion with an appropriately chosen Hurst parameter. Under certain conditions every given linear spectrum can be reproduced using this construction. Moreover, a wide range of Legendre spectra can be arbitrarily closely approximated. The properties of the model are also discussed and the possible use of the model is shown in a simulation study