The Discrete Laguerre Polynomials and Their Use in Exponential Smoothing

The formulation and methodology of curve fitting polynomials by discounted least squares can be simplified through the use of the discrete Laguerre polynomials, which are mutually orthogonal with respect to an exponential weighting function. One advantage of this formulation is that the first k+ 1 coefficients of a fitting polynomial of degree m > k are the same as those of a fitting polynomial of degree k. The Laguerre polynomials are introduced and their properties are derived. The recursive method for computing coefficients is shown to have a simple structure that is independent of the degree k of the fitting polynomials. In addition, some properties of the method of smoothing and forecasting are discussed.