  We analyze quantitatively the effect of spurious multifractality induced by
the presence of fat-tailed symmetric and asymmetric probability distributions
of fluctuations in time series. In the presented approach different kinds of
symmetric and asymmetric broad probability distributions of synthetic data are
examined starting from Levy regime up to those with finite variance. We use
nonextensive Tsallis statistics to construct all considered data in order to
have good analytical description of frequencies of fluctuations in the whole
range of their magnitude and simultaneously the full control over exponent of
power-law decay for tails of probability distribution. The semi-analytical
compact formulas are then provided to express the level of spurious
multifractality generated by the presence of fat tails in terms of Tsallis
parameter $\tilde{q}$ and the scaling exponent $\beta$ of the asymptotic decay
of cumulated probability density function (CDF).The results are presented in
Hurst and H\"{o}lder languages - more often used in study of multifractal
phenomena. According to the provided semi-analytical relations, it is argued
how one can make a clear quantitative distinction for any real data between
true multifractality caused by the presence of nonlinear correlations, spurious
multifractality generated by fat-tailed shape of distributions - eventually
with their asymmetry, and the correction due to linear autocorrelations in
analyzed time series of finite length. In particular, the spurious multifractal
effect of fat tails is found basic for proper quantitative estimation of all
spurious multifractal effects. Examples from stock market data are presented to
support these findings.
