A Simplified Derivation of Linear Least Square Smoothing and Prediction Theory

Abstract

The central results of the Wiener-Kolmogoroff smoothing and prediction theory for stationary time series are developed by a new method. The approach is motivated by physical considerations based on electric circuit theory and does not involve integral equations or the autocorrelation function. The cases treated are the "infinite lag" smoothing problem, the case of pure prediction (without noise), and the general smoothing prediction problem. Finally, the basic assumptions of the theory are discussed in order to clarify the question of when the theory will be appropriate, and to avoid possible misapplication.