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Summary Under certain conditions, the predictors of Integrated Moving Average processes, Markov Polynomial processes, Multiple Exponential Smoothing models and Exponentially Weighted Regression models are identical. In this paper, these conditions are determined and some implications and generalizations are examined.

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In recent years considerable interest has centred on a family of moving average models proposed by Box and Jenkins (1970) for the description of time series which contain a seasonal component. A method is given in the paper for estimating the parameters of the seasonal models based on a principle due to Walker (1961) for the estimation of non-zero members of the autocorrelation function. An illustration of the method is given.