# title
EOF-based linear prediction algorithm: Theory

# abstract
This study considers the theory of a general three-dimensional (space and time) statistical prediction/extrapolation algorithm. The predictor is in the form of a linear data filter. The prediction kernel is based on the minimization of prediction error and its construction requires the covariance statistics of a predictand field. The algorithm is formulated in terms of the spatiotemporal EOFs of the predictand field. This EOF representation facilitates the selection of useful physical modes for prediction. Limited tests have been conducted concerning the sensitivity of the prediction algorithm with respect to its construction parameters and the record length of available data for constructing a covariance matrix. Tests reveal that the performance of the predictor is fairly insensitive to a wide range of the construction parameters. The accuracy of the filter, however, depends strongly on the accuracy of the covariance matrix, which critically depends on the length of available data. This inaccuracy implies suboptimal performance of the prediction filter. Simple examples demonstrate the utility of the new algorithm.