Marco Zamparo — Politecnico di Torino #
Apparent multifractality of self-similar Levy processes #
Scaling properties of time series are usually studied in terms of the
scaling laws of empirical moments, which are the time average estimates of
moments of the dynamic variable. Nonlinearities in the scaling function of
empirical moments are generally regarded as a sign of multifractality in the
data. However, this method fails to disclose the correct monofractal nature
of self-similar Levy processes, except for the Brownian motion. I prove that
for this class of processes it produces apparent multifractality characterised by
a piecewise-linear scaling function with two different regimes, which match at
the stability index of the considered process.