  We investigate the presence of residual multifractal background for
monofractal signals which appears due to the finite length of the signals and
(or) due to the long memory the signals reveal. This phenomenon is investigated
numerically within the multifractal detrended fluctuation analysis (MF-DFA) for
artificially generated time series. Next, the analytical formulas enabling to
describe the multifractal content in such signals are provided. Final results
are shown in the frequently used generalized Hurst exponent h(q) multifractal
scenario and are presented as a function of time series length L and the
autocorrelation exponent value {\gamma}. The multifractal spectrum ({\alpha}, f
({\alpha})) approach is also discussed. The obtained results may be significant
in any practical application of multifractality, including financial data
analysis, because the "true" multifractal effect should be clearly separated
from the so called "multifractal noise". Examples from finance in this context
are given. The provided formulas may help to decide whether we do deal with the
signal of real multifractal origin or not.
