The Autocovariance Function Determined Via the Z-Transform,with Application to Box Jenkins Forecasting Models.

摘要

A Method is presented which yields the autocovariance function of a stationary discrete-time stochastic process in closed form. Special reference is made to the Box Jenkins forecasting methodology in which the underlying process is generated by passing white noise through a linear filter. The impulse response of the filter and its Z-transform, the transfer function, are obtained from the equation which defines the filter. The bilateral Z-transform of the autocovariance function is then derived from the transfer function, and is inverted following a partially fraction expansion. Several examples of this procedure are worked out in detail, and a summary of solutions for a number of cases is given. (Author)