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The Multi-Fractal Model of Asset Returns: Simple Moment and GMM Estimation

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  • Thomas Lux

Abstract

Multi-fractal processes have been proposed as a new formalism for modelling the time series of returns in finance. The major attraction of these processes is their capability of generating various degrees of long-memory in different powers of returns - a feature that has been found to characterise virtually all financial prices. Furthermore, elementary variants of multi-fractal models are very parsimonious formalisations as they are essentially one-parameter families of stochastic processes. The aim of this paper is to provide a first assessment of the goodness-of-fit of this new class of models by applying them to four long time series from different financial markets (one exchange rate, two stock market indices and the price of gold). To this end, we complement the heuristic estimation methods from statistical physics by developing a GMM (Generalised Method of Moment) estimator for the Binomial and Lognormal multifractal models. Our results are very encouraging in that the estimated models provide an astonishingly good fit to the unconditional distribution of the data. Applying Hansen's test, we are, in fact, unable in three out of four cases to reject the multi-fractal model.

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2001 with number 62.

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Date of creation: 01 Apr 2001
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Handle: RePEc:sce:scecf1:62

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Keywords: multi-fractality; long-range dependence; Hñlder spectrum;

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Cited by:
  1. Laurent Calvet & Adlai Fisher, 2003. "Regime-Switching and the Estimation of Multifractal Processes," NBER Working Papers 9839, National Bureau of Economic Research, Inc.

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