Adaptive predictor of numerical sequences, based on linear stationary digital filter, demonstrates some signs of "intelligent" behavior, despite the simplicity of the algorithm, which signs have been illustrated on test numerical sequences. The numerical sequence which is subject to the forecast, turns out as a result of periodic selection and is being passed via the linear continuous time digital filter in real time. The received on an output value of the filter is the current forecast of the same sequence for a certain amount of clock periods forward. Impulse responses of the filter are automatically set up by the unit of numerical optimization on a minimum of a root mean square error of the forecast for previously received information. This process of setup, so-called self-training or adaptation, precedes to the forecast itself. In the course of self-training the algorithm automatically reveals the hidden trends, frequencies and regularities of the process and uses them for the forecast.