Exponential Smoothing Methods of Forecasting and General ARMA Time Series Representations

The focus of this paper is on the relationship between the exponential smoothing methods of forecasting and the integrated autoregressive-moving average models underlying them. In this paper we derive, for the first time, the general linear relationship between their parameters. A method, suitable for implementation on computer, is proposed to determine the pertinent quantities in this relationship. It is illustrated on common forms of exponential smoothing. It is also applied to a new seasonal form of exponential smoothing with seasonal indexes which always sum to zero.