  We achieve the multifractal analysis of a class of complex valued
statistically self-similar continuous functions. For we use multifractal
formalisms associated with pointwise oscillation exponents of all orders. Our
study exhibits new phenomena in multifractal analysis of continuous functions.
In particular, we find examples of statistically self-similar such functions
obeying the multifractal formalism and for which the support of the singularity
spectrum is the whole interval $[0,\infty]$.
