The Finite Memory Prediction of Covariance Stationary Time Series.

An algorithm is presented for conveniently calculating h step ahead minimum mean square linear predictors and prediction variances given a finite number of observations from a covariance stationary time series Y. It is shown that elements of the modified Cholesky decomposition of the covariance matrix of observations play the role in finite memory prediction that the coefficients in the infinite order moving average representation of Y play in infinite memory prediction. The algorithm is applied to autoregressive-moving average time series where further simplifications are shown to occur. A numerical example illustrating the basic points of the general algorithm is presented. Author