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Condensed Matter and Complex Systems

Eur. Phys. J. B 13, 595-599

Apparent multifractality in financial time series

J.-P. Bouchaud1,2 - M. Potters1 - M. Meyer1

1 Science & Finance, 109-111 rue Victor Hugo, 92532 Levallois Cedex, France
2 Service de Physique de l'État Condensé, Centre d'études de Saclay, Orme des Merisiers,
91191 Gif-sur-Yvette Cedex, France

Received 30 June 1999

We present a exactly soluble model for financial time series that mimics the long range volatility correlations known to be present in financial data. Although our model is asymptotically `monofractal' by construction, it shows apparent multiscaling as a result of a slow crossover phenomenon on finite time scales. Our results suggest that it might be hard to distinguish apparent and true multifractal behavior in financial data. Our model also leads to a new family of stable laws for sums of correlated random variables.

02.50.-r Probability theory, stochastic processes, and statistics - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 89.90.+n Other topics of general interest to physicists (restricted to new topics in section 89)

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