Can averaged orbits be used to extract scaling functions?

Trajectory scaling functions are the basic element in the study of chaotic dynamical systems, from which any long time average can be computed. It has never been extracted from an experimental time series the reason being its sensitivity to noise. It is shown, by numerical simulations, that the sensitivity of the scaling function is to drift in the control parameters, and not noise. It is also explained how naive averaging of the orbit points may lead to erroneous results.