Extensions of the Fundamental Theorem of Exponential Smoothing

The fundamental theorem of exponential smoothing is extended to include the nonasymptotic case where only a finite number of time series observations are available. This extension leads to the rigorous elimination of the present need for initial conditions in general order exponential smoothing forecasts. In addition, a computationally efficient procedure is presented for the calculation of all elements of the general order exponential smoothing coefficient matrix. These extensions of the fundamental theorem permit the applied use of general order exponential smoothing in a computationally efficient and unambiguous manner.