Abstract
Weakly nonstationary processes appear in many challenging problems related to the physics of complex systems. An interesting question is how to quantify the rate of convergence to Gaussian behavior of rescaled heteroscedastic time series with stationary first moments but nonstationary multifractal long-range correlated second moments. Here we use the approach which uses a recently proposed extension of the Lévy sections theorem. We analyze statistical and multifractal properties of heteroscedastic time series and find that the Lévy sections approach provides a faster convergence to Gaussian behavior relative to the convergence of traditional partial sums of variables. We also observe that the rescaled signals retain multifractal properties even after reaching what appears to be the stable Gaussian regime.