  We study quantitatively the level of false multifractal signal one may
encounter while analyzing multifractal phenomena in time series within
multifractal detrended fluctuation analysis (MF-DFA). The investigated effect
appears as a result of finite length of used data series and is additionally
amplified by the long-term memory the data eventually may contain. We provide
the detailed quantitative description of such apparent multifractal background
signal as a threshold in spread of generalized Hurst exponent values $\Delta h$
or a threshold in the width of multifractal spectrum $\Delta \alpha$ below
which multifractal properties of the system are only apparent, i.e. do not
exist, despite $\Delta\alpha\neq0$ or $\Delta h\neq 0$. We find this effect
quite important for shorter or persistent series and we argue it is linear with
respect to autocorrelation exponent $\gamma$. Its strength decays according to
power law with respect to the length of time series. The influence of basic
linear and nonlinear transformations applied to initial data in finite time
series with various level of long memory is also investigated. This provides
additional set of semi-analytical results. The obtained formulas are
significant in any interdisciplinary application of multifractality, including
physics, financial data analysis or physiology, because they allow to separate
the 'true' multifractal phenomena from the apparent (artificial) multifractal
effects. They should be a helpful tool of the first choice to decide whether we
do in particular case with the signal with real multiscaling properties or not.
