The method of extrapolating asymptotic series, based on the self-similar ap
proximation theory, is developed. Several important questions are answered,
which makes the foundation of the method unambiguous and its application s
traightforward. It is shown how the extrapolation of asymptotic series can
be reformulated as forecasting for time series. The probability measure is
introduced characterizing the ensemble of forecasted scenarios. The method
of choosing the complete family of databases is put forward.