We investigate the presence of multifractal residual background effect for pre-assumed monofractal signals, appearing due to the finite length of the signal and (or) due to the long memory the signal reveals. This phenomenon is investigated numerically for time series artificially generated with various methods. Next, analytical formulae enabling to describe their multifractal content are provided. Final results are shown as the function of time series length and the long memory exponent in two frequently used multifractal languages, i.e.: generalized Hurst exponent h(q) and Holder multifractal spectrum width scenario. The obtained results may be significant in any practical application of multifractality, including financial data analysis, because the "true" multifractal effect can be clearly separated from the so called "multifractal noise". This way one may easy decide whether we do deal with the signal of multifractal origin or not.

1. PRESENTATION: Multifractal background of monofractal finite signals with long memory, PDF document, version 1.4, 0.8MB

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