SFB 303 Discussion Paper No. B - 456
Author: Lux, Thomas
Title: Multi-Fractal Processes as Models for Financial Returns: A First Assessment
Abstract: Multi-fractal processes have been proposed as a new formalism for
modeling 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 characterize virtually all
financial prices. Furthermore, elementary variants of multi-fractal models
are very parsimonious
formalizations 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). Our
results are very encouraging in that the estimated models provide an
astonishingly good fit to the unconditional
distribution of the data and do even outperform estimates from a GARCH(1,1)
specification. However, we also
remark that a trade-off exists between goodness
-of-fit for the unconditional distribution and the capability of the
estimated processes to match the
autocorrelation patterns of various moments.
Keywords: multi-fractality, long-range dependence, Hölder spectrum
JEL-Classification-Number: C20, G12
Creation-Date: August 1999
URL: ../1999/b/bonnsfb456.pdf
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