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

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  • James M. Dobbie

    (Arthur D. Little, Inc., Cambridge, Massachusetts)

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.

Suggested Citation

  • James M. Dobbie, 1963. "Letter to the Editor---A Simple Proof of a Theorem in Exponential Smoothing," Operations Research, INFORMS, vol. 11(3), pages 461-463, June.
    • Handle: RePEc:inm:oropre:v:11:y:1963:i:3:p:461-463
    DOI: 10.1287/opre.11.3.461
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