  The robustness of two widespread multifractal analysis methods, one based on
detrended fluctuation analysis and one on wavelet leaders, is discussed in the
context of time-series containing non-uniform structures with only isolated
singularities. Signals generated by simulated and experimentally-realized chaos
generators, together with synthetic data addressing particular aspects, are
taken into consideration. The results reveal essential limitations affecting
the ability of both methods to correctly infer the non-multifractal nature of
signals devoid of a cascade-like hierarchy of singularities. Namely, signals
harboring only isolated singularities are found to artefactually give rise to
broad multifractal spectra, resembling those expected in the presence of a
well-developed underlying multifractal structure. Hence, there is a real risk
of incorrectly inferring multifractality due to isolated singularities. The
careful consideration of local scaling properties and the distribution of
H\"older exponent obtained, for example, through wavelet analysis, is
indispensable for rigorously assessing the presence or absence of
multifractality.
