Apparent multifractality in financial time series

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. PACS. 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) Many time series exhibit interesting scaling properties. This means that if x(t) denotes the time series, the probability distribution of the variations δTx = x(t+T )−x(t), rescaled by a lag-dependent factor ξ(T ), can be written as: