  A defining feature of non-stationary systems is the time dependence of their
statistical parameters. Measured time series may exhibit Gaussian statistics on
short time horizons, due to the central limit theorem. The sample statistics
for long time horizons, however, averages over the time-dependent parameters.
To model the long-term statistical behavior, we compound the local distribution
with the distribution of its parameters. Here we consider two concrete, but
diverse examples of such non-stationary systems, the turbulent air flow of a
fan and a time series of foreign exchange rates. Our main focus is to
empirically determine the appropriate parameter distribution for the
compounding approach. To this end we have to estimate the parameter
distribution for univariate time series in a highly non-stationary situation.
