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.
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Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number
456.
Length: pages Date of creation: Aug 1999 Date of revision: Handle: RePEc:bon:bonsfb:456
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Find related papers by JEL classification: C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
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