A Method for Determining the Autocoyariance Function of A Box-Jenkins Forecasting Model

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Abstract
A method is presented for finding closed form expressions of the autocovariance function of a Box-Jenkins forecasting model. This method is based on the filter impulse response and its Z-transform, the transfer function. The bilateral Z-transform of the autocovariance function is obtained from the transfer function, and is inverted after a partial fraction expansion. One example is worked out in detail and a summary of solutions for a number of cases is given.

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