General exponential smoothing and the equivalent arma process

Although the basic principles of exponential smoothing and discounted least squares are easily understood, the full power of the technique is only rarely exploited. The reason for this failure lies in the complexity of the standard procedures. Often they require fairly complex mathematical models and use a variety of cumbersome algebraic manipulations. An alternative formulation for exponential smoothing is presented. It simplifies these procedures and allows an easier use of the full range of models. This new formulation is obtained by considering the relationship between general exponential smoothing (GES) and the well-known ARMA process of Box and Jenkins. The three commonest seasonal models have only recently been considered for GES systems. They are discussed in some detail here. The computational requirements of the GES and equivalent ARMA procedures are reviewed and some recommendations for their application are made. The initialization of GES forecasting systems and the important problem of model selection is also discussed. A brief illustrative example is given.