  Share price returns on different time scales can be well modelled by a
superstatistical dynamics. Here we provide an investigation which type of
superstatistics is most suitable to properly describe share price dynamics on
various time scales. It is shown that while chi-square superstatistics works
well on a time scale of days, on a much smaller time scale of minutes the price
changes are better described by lognormal superstatistics. The system dynamics
thus exhibits a transition from lognormal to chi-square superstatistics as a
function of time scale. We discuss a more general model interpolating between
both statistics which fits the observed data very well. We also present results
on correlation functions of the extracted superstatistical volatility
parameter, which exhibits exponential decay for returns on large time scales,
whereas for returns on small time scales there are long-range correlations and
power-law decay.
