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Multifractal analysis of foreign exchange data

✍ Scribed by Schmitt, François ;Schertzer, Daniel ;Lovejoy, Shaun

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
267 KB
Volume
15
Category
Article
ISSN
8755-0024

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✦ Synopsis

In this paper we perform multifractal analyses of "ve daily Foreign Exchange (FX) rates. These techniques are currently used in turbulence to characterize scaling and intermittency. We show the multifractal nature of FX returns, and estimate the three parameters in the universal multifactal framework, which characterize all small and medium intensity #uctuations, at all scales. For large #uctuations, we address the question of hyperbolic (fat) tails of the distributions which are characterized by a fourth parameter, the tail index. We studied both the prices #uctuations and the returns, "nding no systematic di!erence in the scaling exponents in the two cases.

We discuss and compare our results with several recent studies, and show how the additive models are not compatible with data: Brownian, fractional Brownian, LeH vy, Truncated LeH vy and fractional LeH vy models. We analyse in this framework the ARCH(1), GARCH(1, 1) and HARCH (7) models, and show that their structure functions scaling exponents are undistinguishable from that of Brownian motion, which means that these models do not adequately describe the scaling properties of the statistics of the data.

Our results indicate that there might exist a multiplicative &#ux of "nancial information', which conditions small-scale statistics to large-scale values, as an analogy with the energy #ux in turbulence.

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