Theoretical fundamentals and information aspects of method of extrapolation of short-term time series, based on idea of prolongation of analytical functions out of limits of initial temporal measurements area are stated in this work. The nature of predicted data is considered by using special criteria for the length of taken datasets, based on recurrence plots method, which gives an opportunity to estimate the predictability of observed time series via the determinism of the system. Results of the experimental functional test of a method on examples of real financial series are given. The description of algorithm and data segment length selection criteria is provided as well. Thus, such combination of methods of adaptive extrapolation and complex systems dynamic approach is a rather useful addition to other well known methods of time series analysis and prediction, especially when their effectiveness appears to be very poor.