Letter to the Editor---A Simple Proof of a Theorem in Exponential Smoothing

James M. Dobbie
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James M. Dobbie: Arthur D. Little, Inc., Cambridge, Massachusetts

Operations Research, 1963, vol. 11, issue 3, 461-463

Abstract: A simple proof is given of a theorem in exponential smoothing that is sometimes referred to as “the fundamental theorem”. This theorem states that a polynomial, of degree N at most, minimizes the exponentially-discounted sum of squares of the errors if and only if it satisfies the set of N + 1 equations obtained by equating the i th iteration of the exponentially-discounted average of the sequence to the corresponding average of the polynomial, i = 1, 2, ..., N + 1.

Date: 1963
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