An Analysis of General Exponential Smoothing

General exponential smoothing and adaptive smoothing are terms used to describe the application of discounted least squares to the fitting of certain mathematical functions to time series data. The technique yields forecasts satisfying simple recursive equations that generally contain fairly complex terms. We obtain the transfer function of such forecasting systems and derive from it an equivalent but simpler and more economic forecasting system. Other advantages of using the transfer function form for these complicated forecasting systems are discussed from both theoretical and computational viewpoints.