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.