Stability of a Method of Smoothing in a Digital Control Computer

In a certain operation a digital computer was used as an element of a control system to smooth consecutive observational data. The method of smoothing consisted of predicting from past smoothed values and then combining the prediction with the next observation. In this paper an analysis of the stability of this useful method is made, and an explicit formula of the range of the parameters for which the method is stable is derived. Also, the statistical variance of the smoothed variable is calculated.