  The method of extrapolating asymptotic series, based on the Self-Similar
Approximation Theory, is developed. Several important questions are answered,
which makes the foundation of the method unambiguous and its application
straightforward. 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 way of
choosing the complete family of data bases is advanced.
