Multifractal analysis of foreign exchange data chains. (English) Zbl 0927.62110
The authors adopted the multifractal approach, which was successfully used in investigations of turbulence, to the analysis of five daily foreign exchange (FX) data. This method takes into account two complementary aspects of financial time series: the multiple scaling and hyperbolic (Pareto-type) probability distributions. The so-called scale invariant structure exponent \(\xi(q)\) is proposed as a good tool for studying the scaling behaviour of fluctuations of time series. The corresponding analysis both of price data and the logarithm of prices makes no significant difference for \(\xi(q)\) in these two cases. A further comparison with popular additive models (Brownian, fractional Brownian, Lévy, fractional Lévy) and several types of ARCH, GARCH and HARCH models hase been carried out. The authors underline the advantages of multiplicative models in comparison with additive ones and hope that multifractal techniques will be useful in investigation of financial data.
Reviewer: N.M.Zinchenko (Kyïv)
MSC:
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
| 91B28 | Finance etc. (MSC2000) |
| 62M99 | Inference from stochastic processes |
Keywords:
financial time series; foreign exchange; scaling; multifractals; additive models; multiplicative models; Pareto-type distributionsReferences:
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